diff --git a/ext/gmp/gmp.c b/ext/gmp/gmp.c
index c9603c8fb21e8..7669d76dc73f4 100644
--- a/ext/gmp/gmp.c
+++ b/ext/gmp/gmp.c
@@ -47,6 +47,12 @@
 #define GMP_BIG_ENDIAN    (1 << 3)
 #define GMP_NATIVE_ENDIAN (1 << 4)
 
+#if SIZEOF_SIZE_T == 4
+#define GMP_ALLOC_MAXBITS (ULONG_MAX / GMP_NUMB_BITS)
+#else
+#define GMP_ALLOC_MAXBITS INT_MAX
+#endif
+
 #include "gmp_arginfo.h"
 
 ZEND_DECLARE_MODULE_GLOBALS(gmp)
@@ -1276,14 +1282,17 @@ ZEND_FUNCTION(gmp_fact)
 {
 	zval *a_arg;
 	mpz_ptr gmpnum_result;
+	zend_long val;
 
 	if (zend_parse_parameters(ZEND_NUM_ARGS(), "z", &a_arg) == FAILURE){
 		RETURN_THROWS();
 	}
 
+
 	if (Z_TYPE_P(a_arg) == IS_LONG) {
-		if (Z_LVAL_P(a_arg) < 0) {
-			zend_argument_value_error(1, "must be greater than or equal to 0");
+		val = Z_LVAL_P(a_arg);
+		if (val < 0 || val > GMP_ALLOC_MAXBITS) {
+			zend_argument_value_error(1, "must be between 0 and " ZEND_LONG_FMT, GMP_ALLOC_MAXBITS);
 			RETURN_THROWS();
 		}
 	} else {
@@ -1293,14 +1302,16 @@ ZEND_FUNCTION(gmp_fact)
 		FETCH_GMP_ZVAL(gmpnum, a_arg, temp_a, 1);
 		FREE_GMP_TEMP(temp_a);
 
-		if (mpz_sgn(gmpnum) < 0) {
-			zend_argument_value_error(1, "must be greater than or equal to 0");
+		(void)gmpnum;
+		val = zval_get_long(a_arg);
+		if (val < 0 || val > GMP_ALLOC_MAXBITS) {
+			zend_argument_value_error(1, "must be between 0 and " ZEND_LONG_FMT, GMP_ALLOC_MAXBITS);
 			RETURN_THROWS();
 		}
 	}
 
 	INIT_GMP_RETVAL(gmpnum_result);
-	mpz_fac_ui(gmpnum_result, zval_get_long(a_arg));
+	mpz_fac_ui(gmpnum_result, val);
 }
 /* }}} */
 
@@ -1859,14 +1870,8 @@ ZEND_FUNCTION(gmp_random_bits)
 		RETURN_THROWS();
 	}
 
-#if SIZEOF_SIZE_T == 4
-	const zend_long maxbits = ULONG_MAX / GMP_NUMB_BITS;
-#else
-	const zend_long maxbits = INT_MAX;
-#endif
-
-	if (bits <= 0 || bits > maxbits) {
-		zend_argument_value_error(1, "must be between 1 and " ZEND_LONG_FMT, maxbits);
+	if (bits <= 0 || bits > GMP_ALLOC_MAXBITS) {
+		zend_argument_value_error(1, "must be between 1 and " ZEND_LONG_FMT, GMP_ALLOC_MAXBITS);
 		RETURN_THROWS();
 	}
 
diff --git a/ext/gmp/tests/gh16878.phpt b/ext/gmp/tests/gh16878.phpt
new file mode 100644
index 0000000000000..566931cd06b7d
--- /dev/null
+++ b/ext/gmp/tests/gh16878.phpt
@@ -0,0 +1,21 @@
+--TEST--
+GH-16878 (gmp_fact overflow)
+--EXTENSIONS--
+gmp
+--FILE--
+<?php
+try {
+	gmp_fact(PHP_INT_MAX);
+} catch (\ValueError $e) {
+	echo $e->getMessage() . PHP_EOL;
+}
+
+try {
+	gmp_fact(gmp_init(PHP_INT_MAX));
+} catch (\ValueError $e) {
+	echo $e->getMessage();
+}
+?>
+--EXPECTF--
+gmp_fact(): Argument #1 ($num) must be between 0 and %d
+gmp_fact(): Argument #1 ($num) must be between 0 and %d
diff --git a/ext/gmp/tests/gmp_fact.phpt b/ext/gmp/tests/gmp_fact.phpt
index e039314549405..b28f572c6975a 100644
--- a/ext/gmp/tests/gmp_fact.phpt
+++ b/ext/gmp/tests/gmp_fact.phpt
@@ -45,17 +45,17 @@ try {
 
 echo "Done\n";
 ?>
---EXPECT--
+--EXPECTF--
 string(1) "1"
 gmp_fact(): Argument #1 ($num) is not an integer string
 string(1) "1"
-gmp_fact(): Argument #1 ($num) must be greater than or equal to 0
-gmp_fact(): Argument #1 ($num) must be greater than or equal to 0
+gmp_fact(): Argument #1 ($num) must be between 0 and %d
+gmp_fact(): Argument #1 ($num) must be between 0 and %d
 string(19) "2432902008176640000"
 string(65) "30414093201713378043612608166064768844377641568960512000000000000"
 string(7) "3628800"
 string(1) "1"
 string(9) "479001600"
-gmp_fact(): Argument #1 ($num) must be greater than or equal to 0
+gmp_fact(): Argument #1 ($num) must be between 0 and %d
 gmp_fact(): Argument #1 ($num) must be of type GMP|string|int, array given
 Done