diff --git a/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/Reducer.java b/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/Reducer.java
index 5f3c3385a9431..af742fe8cb24a 100644
--- a/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/Reducer.java
+++ b/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/Reducer.java
@@ -21,13 +21,20 @@
 /**
  * A 'reducer' for output of user-defined functions.
  *
- * A user_defined function f_source(x) is 'reducible' on another user_defined function f_target(x),
- * if there exists a 'reducer' r(x) such that r(f_source(x)) = f_target(x) for all input x.
+ * @see ReducibleFunction
+ *
+ * A user defined function f_source(x) is 'reducible' on another user_defined function f_target(x) if
+ * <ul>
+ *   <li> There exists a reducer function r(x) such that r(f_source(x)) = f_target(x) for all input x. </li>
+ *   <li> More generally, there exists two reducer functions r1(x) and r2(x) such that
+ *     r1(f_source(x)) = r2(f_target(x)) for all input x. </li>
+ * </ul>
+ *
  * @param <I> reducer input type
  * @param <O> reducer output type
  * @since 4.0.0
  */
 @Evolving
 public interface Reducer<I, O> {
-    O reduce(I arg1);
+    O reduce(I arg);
 }
diff --git a/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/ReducibleFunction.java b/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/ReducibleFunction.java
index 6d57909e1b984..9d2215c1167cc 100644
--- a/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/ReducibleFunction.java
+++ b/sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/ReducibleFunction.java
@@ -17,23 +17,34 @@
 package org.apache.spark.sql.connector.catalog.functions;
 
 import org.apache.spark.annotation.Evolving;
-import scala.Option;
 
 /**
  * Base class for user-defined functions that can be 'reduced' on another function.
  *
  * A function f_source(x) is 'reducible' on another function f_target(x) if
- * there exists a reducer function r(x) such that r(f_source(x)) = f_target(x) for all input x.
- *
+ * <ul>
+ *   <li> There exists a reducer function r(x) such that r(f_source(x)) = f_target(x) for all input x. </li>
+ *   <li> More generally, there exists two reducer functions r1(x) and r2(x) such that
+ *        r1(f_source(x)) = r2(f_target(x)) for all input x. </li>
+ * </ul>
  * <p>
  * Examples:
  * <ul>
- *    <li>Bucket functions
+ *    <li>Bucket functions where one side has reducer
  *    <ul>
  *        <li>f_source(x) = bucket(4, x)</li>
  *        <li>f_target(x) = bucket(2, x)</li>
- *        <li>r(x) = x / 2</li>
+ *        <li>r(x) = x % 2</li>
  *    </ul>
+ *
+ *    <li>Bucket functions where both sides have reducer
+ *    <ul>
+ *        <li>f_source(x) = bucket(16, x)</li>
+ *        <li>f_target(x) = bucket(12, x)</li>
+ *        <li>r1(x) = x % 4</li>
+ *        <li>r2(x) = x % 4</li>
+ *    </ul>
+ *
  *    <li>Date functions
  *    <ul>
  *        <li>f_source(x) = days(x)</li>
@@ -49,24 +60,42 @@
 public interface ReducibleFunction<I, O> {
 
     /**
-     * If this function is 'reducible' on another function, return the {@link Reducer} function.
+     * This method is for bucket functions.
+     *
+     * If this bucket function is 'reducible' on another bucket function, return the {@link Reducer} function.
      * <p>
-     * Example:
+     * Example to return reducer for reducing f_source = bucket(4, x) on f_target = bucket(2, x)
      * <ul>
-     *     <li>this_function = bucket(4, x)
-     *     <li>other function = bucket(2, x)
+     *     <li>thisFunction = bucket</li>
+     *     <li>otherFunction = bucket</li>
+     *     <li>thisNumBuckets = Int(4)</li>
+     *     <li>otherNumBuckets = Int(2)</li>
      * </ul>
-     * Invoke with arguments
+     *
+     * @param otherFunction the other bucket function
+     * @param thisNumBuckets number of buckets for this bucket function
+     * @param otherNumBuckets number of buckets for the other bucket function
+     * @return a reduction function if it is reducible, null if not
+     */
+    default Reducer<I, O> reducer(ReducibleFunction<?, ?> otherFunction, int thisNumBuckets, int otherNumBuckets) {
+        return reducer(otherFunction);
+    }
+
+    /**
+     * This method is for all other functions.
+     *
+     * If this function is 'reducible' on another function, return the {@link Reducer} function.
+     * <p>
+     * Example of reducing f_source = days(x) on f_target = hours(x)
      * <ul>
-     *     <li>other = bucket</li>
-     *     <li>this param = Int(4)</li>
-     *     <li>other param = Int(2)</li>
+     *     <li>thisFunction = days</li>
+     *     <li>otherFunction = hours</li>
      * </ul>
-     * @param other the other function
-     * @param thisParam param for this function
-     * @param otherParam param for the other function
-     * @return a reduction function if it is reducible, none if not
+     *
+     * @param otherFunction the other function
+     * @return a reduction function if it is reducible, null if not.
      */
-    Option<Reducer<I, O>> reducer(ReducibleFunction<?, ?> other, Option<?> thisParam,
-                               Option<?> otherParam);
+    default Reducer<I, O> reducer(ReducibleFunction<?, ?> otherFunction) {
+        return reducer(otherFunction, 0, 0);
+    }
 }
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/TransformExpression.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/TransformExpression.scala
index 5dc048f5dafbd..eff0a0ddfe71b 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/TransformExpression.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/TransformExpression.scala
@@ -70,9 +70,10 @@ case class TransformExpression(
     } else {
       (function, other.function) match {
         case (f: ReducibleFunction[_, _], o: ReducibleFunction[_, _]) =>
-          val reducer = f.reducer(o, numBucketsOpt, other.numBucketsOpt)
-          val otherReducer = o.reducer(f, other.numBucketsOpt, numBucketsOpt)
-          reducer.isDefined || otherReducer.isDefined
+          val reducer = f.reducer(o, numBucketsOpt.getOrElse(0), other.numBucketsOpt.getOrElse(0))
+          val otherReducer =
+            o.reducer(f, other.numBucketsOpt.getOrElse(0), numBucketsOpt.getOrElse(0))
+          reducer != null || otherReducer != null
         case _ => false
       }
     }
@@ -90,7 +91,10 @@ case class TransformExpression(
   def reducers(other: TransformExpression): Option[Reducer[_, _]] = {
     (function, other.function) match {
       case(e1: ReducibleFunction[_, _], e2: ReducibleFunction[_, _]) =>
-        e1.reducer(e2, numBucketsOpt, other.numBucketsOpt)
+        val reducer = e1.reducer(e2,
+          numBucketsOpt.getOrElse(0),
+          other.numBucketsOpt.getOrElse(0))
+        Option(reducer)
       case _ => None
     }
   }
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
index 0bdb1fde67b22..33ea5ad52cd5c 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
@@ -851,25 +851,23 @@ case class KeyGroupedShuffleSpec(
    * A [[Reducer]] exists for a partition expression function of this shuffle spec if it is
    * 'reducible' on the corresponding partition expression function of the other shuffle spec.
    * <p>
-   * If a value is returned, there must be one Option[[Reducer]] per partition expression.
+   * If a value is returned, there must be one [[Reducer]] per partition expression.
    * A None value in the set indicates that the particular partition expression is not reducible
    * on the corresponding expression on the other shuffle spec.
    * <p>
    * Returning none also indicates that none of the partition expressions can be reduced on the
    * corresponding expression on the other shuffle spec.
+   *
+   * @param other other key-grouped shuffle spec
    */
-  def reducers(other: ShuffleSpec): Option[Seq[Option[Reducer[_, _]]]] = {
-    other match {
-      case otherSpec: KeyGroupedShuffleSpec =>
-        val results = partitioning.expressions.zip(otherSpec.partitioning.expressions).map {
-          case (e1: TransformExpression, e2: TransformExpression) => e1.reducers(e2)
-          case (_, _) => None
-        }
+  def reducers(other: KeyGroupedShuffleSpec): Option[Seq[Option[Reducer[_, _]]]] = {
+     val results = partitioning.expressions.zip(other.partitioning.expressions).map {
+       case (e1: TransformExpression, e2: TransformExpression) => e1.reducers(e2)
+       case (_, _) => None
+     }
 
-        // optimize to not return a value, if none of the partition expressions are reducible
-        if (results.forall(p => p.isEmpty)) None else Some(results)
-      case _ => None
-    }
+    // optimize to not return a value, if none of the partition expressions are reducible
+    if (results.forall(p => p.isEmpty)) None else Some(results)
   }
 
   override def canCreatePartitioning: Boolean = SQLConf.get.v2BucketingShuffleEnabled &&
@@ -883,8 +881,8 @@ case class KeyGroupedShuffleSpec(
 
 object KeyGroupedShuffleSpec {
   def reducePartitionValue(row: InternalRow,
-                           expressions: Seq[Expression],
-                           reducers: Seq[Option[Reducer[_, _]]]):
+    expressions: Seq[Expression],
+    reducers: Seq[Option[Reducer[_, _]]]):
     InternalRowComparableWrapper = {
     val partitionVals = row.toSeq(expressions.map(_.dataType))
     val reducedRow = partitionVals.zip(reducers).map{
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/exchange/EnsureRequirements.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/exchange/EnsureRequirements.scala
index b34990e1b7166..7ff682178ad27 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/execution/exchange/EnsureRequirements.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/exchange/EnsureRequirements.scala
@@ -569,8 +569,8 @@ case class EnsureRequirements(
   }
 
   private def reduceCommonPartValues(commonPartValues: Seq[(InternalRow, Int)],
-                                     expressions: Seq[Expression],
-                                     reducers: Option[Seq[Option[Reducer[_, _]]]]) = {
+    expressions: Seq[Expression],
+    reducers: Option[Seq[Option[Reducer[_, _]]]]) = {
     reducers match {
       case Some(reducers) => commonPartValues.groupBy { case (row, _) =>
         KeyGroupedShuffleSpec.reducePartitionValue(row, expressions, reducers)
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
index 403081b66551e..ec275fe101fd6 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
@@ -1475,6 +1475,168 @@ class KeyGroupedPartitioningSuite extends DistributionAndOrderingSuiteBase {
     }
   }
 
+  test("SPARK-47094: Support compatible buckets with common divisor") {
+    val table1 = "tab1e1"
+    val table2 = "table2"
+
+    Seq(
+      ((6, 4), (4, 6)),
+      ((6, 6), (4, 4)),
+      ((4, 4), (6, 6)),
+      ((4, 6), (6, 4))).foreach {
+      case ((table1buckets1, table1buckets2), (table2buckets1, table2buckets2)) =>
+        catalog.clearTables()
+
+        val partition1 = Array(bucket(table1buckets1, "store_id"),
+          bucket(table1buckets2, "dept_id"))
+        val partition2 = Array(bucket(table2buckets1, "store_id"),
+          bucket(table2buckets2, "dept_id"))
+
+        Seq((table1, partition1), (table2, partition2)).foreach { case (tab, part) =>
+          createTable(tab, columns2, part)
+          val insertStr = s"INSERT INTO testcat.ns.$tab VALUES " +
+            "(0, 0, 'aa'), " +
+            "(0, 0, 'ab'), " + // duplicate partition key
+            "(0, 1, 'ac'), " +
+            "(0, 2, 'ad'), " +
+            "(0, 3, 'ae'), " +
+            "(0, 4, 'af'), " +
+            "(0, 5, 'ag'), " +
+            "(1, 0, 'ah'), " +
+            "(1, 0, 'ai'), " + // duplicate partition key
+            "(1, 1, 'aj'), " +
+            "(1, 2, 'ak'), " +
+            "(1, 3, 'al'), " +
+            "(1, 4, 'am'), " +
+            "(1, 5, 'an'), " +
+            "(2, 0, 'ao'), " +
+            "(2, 0, 'ap'), " + // duplicate partition key
+            "(2, 1, 'aq'), " +
+            "(2, 2, 'ar'), " +
+            "(2, 3, 'as'), " +
+            "(2, 4, 'at'), " +
+            "(2, 5, 'au'), " +
+            "(3, 0, 'av'), " +
+            "(3, 0, 'aw'), " + // duplicate partition key
+            "(3, 1, 'ax'), " +
+            "(3, 2, 'ay'), " +
+            "(3, 3, 'az'), " +
+            "(3, 4, 'ba'), " +
+            "(3, 5, 'bb'), " +
+            "(4, 0, 'bc'), " +
+            "(4, 0, 'bd'), " + // duplicate partition key
+            "(4, 1, 'be'), " +
+            "(4, 2, 'bf'), " +
+            "(4, 3, 'bg'), " +
+            "(4, 4, 'bh'), " +
+            "(4, 5, 'bi'), " +
+            "(5, 0, 'bj'), " +
+            "(5, 0, 'bk'), " + // duplicate partition key
+            "(5, 1, 'bl'), " +
+            "(5, 2, 'bm'), " +
+            "(5, 3, 'bn'), " +
+            "(5, 4, 'bo'), " +
+            "(5, 5, 'bp')"
+
+            // additional unmatched partitions to test push down
+            val finalStr = if (tab == table1) {
+              insertStr ++ ", (8, 0, 'xa'), (8, 8, 'xx')"
+            } else {
+              insertStr ++ ", (9, 0, 'ya'), (9, 9, 'yy')"
+            }
+
+            sql(finalStr)
+        }
+
+        Seq(true, false).foreach { allowJoinKeysSubsetOfPartitionKeys =>
+          withSQLConf(
+            SQLConf.REQUIRE_ALL_CLUSTER_KEYS_FOR_CO_PARTITION.key -> "false",
+            SQLConf.V2_BUCKETING_PUSH_PART_VALUES_ENABLED.key -> "true",
+            SQLConf.V2_BUCKETING_PARTIALLY_CLUSTERED_DISTRIBUTION_ENABLED.key -> "false",
+            SQLConf.V2_BUCKETING_ALLOW_JOIN_KEYS_SUBSET_OF_PARTITION_KEYS.key ->
+              allowJoinKeysSubsetOfPartitionKeys.toString,
+            SQLConf.V2_BUCKETING_ALLOW_COMPATIBLE_TRANSFORMS.key -> "true") {
+            val df = sql(
+              s"""
+                 |${selectWithMergeJoinHint("t1", "t2")}
+                 |t1.store_id, t1.dept_id, t1.data, t2.data
+                 |FROM testcat.ns.$table1 t1 JOIN testcat.ns.$table2 t2
+                 |ON t1.store_id = t2.store_id AND t1.dept_id = t2.dept_id
+                 |ORDER BY t1.store_id, t1.dept_id, t1.data, t2.data
+                 |""".stripMargin)
+
+            val shuffles = collectShuffles(df.queryExecution.executedPlan)
+            assert(shuffles.isEmpty, "SPJ should be triggered")
+
+            val scans = collectScans(df.queryExecution.executedPlan).map(_.inputRDD.
+              partitions.length)
+
+            def gcd(a: Int, b: Int): Int = BigInt(a).gcd(BigInt(b)).toInt
+            val expectedBuckets = gcd(table1buckets1, table2buckets1) *
+              gcd(table1buckets2, table2buckets2)
+            assert(scans == Seq(expectedBuckets, expectedBuckets))
+
+            checkAnswer(df, Seq(
+              Row(0, 0, "aa", "aa"),
+              Row(0, 0, "aa", "ab"),
+              Row(0, 0, "ab", "aa"),
+              Row(0, 0, "ab", "ab"),
+              Row(0, 1, "ac", "ac"),
+              Row(0, 2, "ad", "ad"),
+              Row(0, 3, "ae", "ae"),
+              Row(0, 4, "af", "af"),
+              Row(0, 5, "ag", "ag"),
+              Row(1, 0, "ah", "ah"),
+              Row(1, 0, "ah", "ai"),
+              Row(1, 0, "ai", "ah"),
+              Row(1, 0, "ai", "ai"),
+              Row(1, 1, "aj", "aj"),
+              Row(1, 2, "ak", "ak"),
+              Row(1, 3, "al", "al"),
+              Row(1, 4, "am", "am"),
+              Row(1, 5, "an", "an"),
+              Row(2, 0, "ao", "ao"),
+              Row(2, 0, "ao", "ap"),
+              Row(2, 0, "ap", "ao"),
+              Row(2, 0, "ap", "ap"),
+              Row(2, 1, "aq", "aq"),
+              Row(2, 2, "ar", "ar"),
+              Row(2, 3, "as", "as"),
+              Row(2, 4, "at", "at"),
+              Row(2, 5, "au", "au"),
+              Row(3, 0, "av", "av"),
+              Row(3, 0, "av", "aw"),
+              Row(3, 0, "aw", "av"),
+              Row(3, 0, "aw", "aw"),
+              Row(3, 1, "ax", "ax"),
+              Row(3, 2, "ay", "ay"),
+              Row(3, 3, "az", "az"),
+              Row(3, 4, "ba", "ba"),
+              Row(3, 5, "bb", "bb"),
+              Row(4, 0, "bc", "bc"),
+              Row(4, 0, "bc", "bd"),
+              Row(4, 0, "bd", "bc"),
+              Row(4, 0, "bd", "bd"),
+              Row(4, 1, "be", "be"),
+              Row(4, 2, "bf", "bf"),
+              Row(4, 3, "bg", "bg"),
+              Row(4, 4, "bh", "bh"),
+              Row(4, 5, "bi", "bi"),
+              Row(5, 0, "bj", "bj"),
+              Row(5, 0, "bj", "bk"),
+              Row(5, 0, "bk", "bj"),
+              Row(5, 0, "bk", "bk"),
+              Row(5, 1, "bl", "bl"),
+              Row(5, 2, "bm", "bm"),
+              Row(5, 3, "bn", "bn"),
+              Row(5, 4, "bo", "bo"),
+              Row(5, 5, "bp", "bp")
+            ))
+          }
+        }
+    }
+  }
+
   test("SPARK-47094: Support compatible buckets with less join keys than partition keys") {
     val table1 = "tab1e1"
     val table2 = "table2"
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/connector/catalog/functions/transformFunctions.scala b/sql/core/src/test/scala/org/apache/spark/sql/connector/catalog/functions/transformFunctions.scala
index 7a77c00b577fc..176e597fe44bb 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/connector/catalog/functions/transformFunctions.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/connector/catalog/functions/transformFunctions.scala
@@ -87,21 +87,31 @@ object BucketFunction extends ScalarFunction[Int] with ReducibleFunction[Int, In
   }
 
   override def reducer(func: ReducibleFunction[_, _],
-                       thisNumBuckets: Option[_],
-                       otherNumBuckets: Option[_]): Option[Reducer[Int, Int]] = {
-    (thisNumBuckets, otherNumBuckets) match {
-      case (Some(thisNumBucketsVal: Int), Some(otherNumBucketsVal: Int))
-        if func == BucketFunction &&
-          ((thisNumBucketsVal > otherNumBucketsVal) &&
-            (thisNumBucketsVal % otherNumBucketsVal == 0)) =>
-        Some(BucketReducer(thisNumBucketsVal, otherNumBucketsVal))
-      case _ => None
+    thisNumBuckets: Int,
+    otherNumBuckets: Int): Reducer[Int, Int] = {
+
+    if (func == BucketFunction) {
+      if ((thisNumBuckets > otherNumBuckets)
+        && (thisNumBuckets % otherNumBuckets == 0)) {
+        BucketReducer(thisNumBuckets, otherNumBuckets)
+      } else {
+        val gcd = this.gcd(thisNumBuckets, otherNumBuckets)
+        if (gcd != thisNumBuckets) {
+          BucketReducer(thisNumBuckets, gcd)
+        } else {
+          null
+        }
+      }
+    } else {
+      null
     }
   }
+
+  private def gcd(a: Int, b: Int): Int = BigInt(a).gcd(BigInt(b)).toInt
 }
 
-case class BucketReducer(thisNumBuckets: Int, otherNumBuckets: Int) extends Reducer[Int, Int] {
-  override def reduce(bucket: Int): Int = bucket % otherNumBuckets
+case class BucketReducer(thisNumBuckets: Int, divisor: Int) extends Reducer[Int, Int] {
+  override def reduce(bucket: Int): Int = bucket % divisor
 }
 
 object UnboundStringSelfFunction extends UnboundFunction {