What is the Greatest Common Factor of 89964 and 89976?

Greatest common factor (GCF) of 89964 and 89976 is 12.

GCF(89964,89976) = 12

We will now calculate the prime factors of 89964 and 89976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89964 and 89976.

How to find the GCF of 89964 and 89976?

We will first find the prime factorization of 89964 and 89976. After we will calculate the factors of 89964 and 89976 and find the biggest common factor number .

Step-1: Prime Factorization of 89964

Prime factors of 89964 are 2, 3, 7, 17. Prime factorization of 89964 in exponential form is:

89964 = 2² × 3³ × 7² × 17¹

Step-2: Prime Factorization of 89976

Prime factors of 89976 are 2, 3, 23, 163. Prime factorization of 89976 in exponential form is:

89976 = 2³ × 3¹ × 23¹ × 163¹

Step-3: Factors of 89964

List of positive integer factors of 89964 that divides 89964 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 27, 28, 34, 36, 42, 49, 51, 54, 63, 68, 84, 98, 102, 108, 119, 126, 147, 153, 189, 196, 204, 238, 252, 294, 306, 357, 378, 441, 459, 476, 588, 612, 714, 756, 833, 882, 918, 1071, 1323, 1428, 1666, 1764, 1836, 2142, 2499, 2646, 3213, 3332, 4284, 4998, 5292, 6426, 7497, 9996, 12852, 14994, 22491, 29988, 44982

Step-4: Factors of 89976

List of positive integer factors of 89976 that divides 89964 without a remainder.

1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 138, 163, 184, 276, 326, 489, 552, 652, 978, 1304, 1956, 3749, 3912, 7498, 11247, 14996, 22494, 29992, 44988

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89964 and 89976. The biggest common factor number is the GCF number.
So the greatest common factor 89964 and 89976 is 12.

Also check out the Least Common Multiple of 89964 and 89976