diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java
index ed8323c13..6feb37f34 100644
--- a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java
@@ -71,6 +71,10 @@ public ContinuedFraction() {}
     /**
      * Evaluates the continued fraction.
      *
+     * <p>Uses a default limit on the number of iterations. Use
+     * {@link #evaluate(double,double,int)} to specify an explicit {@code maxIterations}
+     * for a fraction that requires more terms to converge.
+     *
      * @param x the evaluation point.
      * @param epsilon Maximum relative error allowed.
      * @return the value of the continued fraction evaluated at {@code x}.
diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFraction.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFraction.java
index 0b5a0882b..6e33faef1 100644
--- a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFraction.java
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFraction.java
@@ -61,8 +61,15 @@ public final class GeneralizedContinuedFraction {
      * eps * |b_n|, e.g., 1e-50".
      */
     static final double SMALL = 1e-50;
-    /** Default maximum number of iterations. */
-    static final int DEFAULT_ITERATIONS = Integer.MAX_VALUE;
+    /**
+     * Default maximum number of iterations.
+     *
+     * <p>This is bounded well below {@link Integer#MAX_VALUE} so that a fraction which
+     * does not converge fails fast with an exception rather than iterating for an
+     * excessive length of time. A generator that requires more terms than this to
+     * converge should use the overloads that accept an explicit {@code maxIterations}.
+     */
+    static final int DEFAULT_ITERATIONS = 1_000_000;
     /**
      * Minimum relative error epsilon. Equal to 1 - Math.nextDown(1.0), or 2^-53.
      *
@@ -149,6 +156,10 @@ private GeneralizedContinuedFraction() {}
      *
      * <p>Note: The first generated partial numerator a<sub>0</sub> is discarded.
      *
+     * <p>Uses a default limit on the number of iterations. Use
+     * {@link #value(Supplier,double,int)} to specify an explicit {@code maxIterations}
+     * for a fraction that requires more terms to converge.
+     *
      * @param gen Generator of coefficients.
      * @return the value of the continued fraction.
      * @throws ArithmeticException if the algorithm fails to converge or if the maximal number of
@@ -164,6 +175,10 @@ public static double value(Supplier<Coefficient> gen) {
      *
      * <p>Note: The first generated partial numerator a<sub>0</sub> is discarded.
      *
+     * <p>Uses a default limit on the number of iterations. Use
+     * {@link #value(Supplier,double,int)} to specify an explicit {@code maxIterations}
+     * for a fraction that requires more terms to converge.
+     *
      * @param gen Generator of coefficients.
      * @param epsilon Maximum relative error allowed.
      * @return the value of the continued fraction.
@@ -227,6 +242,10 @@ public static double value(Supplier<Coefficient> gen, double epsilon, int maxIte
      *  <li>b<sub>0</sub> is very small and the result is expected to approach zero</li>
      * </ul>
      *
+     * <p>Uses a default limit on the number of iterations. Use
+     * {@link #value(double,Supplier,double,int)} to specify an explicit
+     * {@code maxIterations} for a fraction that requires more terms to converge.
+     *
      * @param b0 Coefficient b<sub>0</sub>.
      * @param gen Generator of coefficients.
      * @return the value of the continued fraction.
@@ -250,6 +269,10 @@ public static double value(double b0, Supplier<Coefficient> gen) {
      *  <li>b<sub>0</sub> is very small and the result is expected to approach zero</li>
      * </ul>
      *
+     * <p>Uses a default limit on the number of iterations. Use
+     * {@link #value(double,Supplier,double,int)} to specify an explicit
+     * {@code maxIterations} for a fraction that requires more terms to converge.
+     *
      * @param b0 Coefficient b<sub>0</sub>.
      * @param gen Generator of coefficients.
      * @param epsilon Maximum relative error allowed.
diff --git a/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFractionTest.java b/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFractionTest.java
index 7eb68237b..256cad386 100644
--- a/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFractionTest.java
+++ b/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/GeneralizedContinuedFractionTest.java
@@ -240,6 +240,46 @@ void testMaxIterationsThrowsB() {
         assertExceptionMessageContains(t, "max");
     }
 
+    /**
+     * Test the default number of iterations is bounded well below
+     * {@link Integer#MAX_VALUE}. A fraction that never converges must fail fast
+     * using the default (no {@code maxIterations} argument) evaluation methods
+     * rather than run for an excessive length of time.
+     *
+     * @see <a href="https://issues.apache.org/jira/browse/NUMBERS-214">NUMBERS-214</a>
+     */
+    @Test
+    void testDefaultIterationsIsBounded() {
+        Assertions.assertTrue(GeneralizedContinuedFraction.DEFAULT_ITERATIONS < Integer.MAX_VALUE / 100,
+            () -> "Default iterations not bounded: " + GeneralizedContinuedFraction.DEFAULT_ITERATIONS);
+    }
+
+    /**
+     * Test that evaluation of a non-converging fraction using the default number of
+     * iterations does not generate substantially more terms than the documented
+     * default limit. This bounds the runtime of a call that omits the
+     * {@code maxIterations} argument.
+     *
+     * @see <a href="https://issues.apache.org/jira/browse/NUMBERS-214">NUMBERS-214</a>
+     */
+    @Test
+    void testNonConvergingFractionUsesDefaultIterationLimit() {
+        // Oscillating generator that never converges:
+        // b0 = 1 seeds the evaluation (a0 is discarded); all subsequent terms
+        // (a=1, b=0) create a non-converging oscillation between two values.
+        final int[] calls = {0};
+        final Supplier<Coefficient> gen = () -> {
+            calls[0]++;
+            return Coefficient.of(1, calls[0] == 1 ? 1 : 0);
+        };
+
+        final Throwable t = Assertions.assertThrows(ArithmeticException.class,
+            () -> GeneralizedContinuedFraction.value(gen));
+        assertExceptionMessageContains(t, "max");
+        Assertions.assertTrue(calls[0] <= GeneralizedContinuedFraction.DEFAULT_ITERATIONS + 1,
+            () -> "Unexpected number of generator calls: " + calls[0]);
+    }
+
     @Test
     void testNaNThrowsA() {
         // Create a NaN during the iteration