What is the Greatest Common Factor of 72996 and 73008?

Greatest common factor (GCF) of 72996 and 73008 is 12.

GCF(72996,73008) = 12

We will now calculate the prime factors of 72996 and 73008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72996 and 73008.

How to find the GCF of 72996 and 73008?

We will first find the prime factorization of 72996 and 73008. After we will calculate the factors of 72996 and 73008 and find the biggest common factor number .

Step-1: Prime Factorization of 72996

Prime factors of 72996 are 2, 3, 7, 11, 79. Prime factorization of 72996 in exponential form is:

72996 = 2² × 3¹ × 7¹ × 11¹ × 79¹

Step-2: Prime Factorization of 73008

Prime factors of 73008 are 2, 3, 13. Prime factorization of 73008 in exponential form is:

73008 = 2⁴ × 3³ × 13²

Step-3: Factors of 72996

List of positive integer factors of 72996 that divides 72996 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 79, 84, 132, 154, 158, 231, 237, 308, 316, 462, 474, 553, 869, 924, 948, 1106, 1659, 1738, 2212, 2607, 3318, 3476, 5214, 6083, 6636, 10428, 12166, 18249, 24332, 36498

Step-4: Factors of 73008

List of positive integer factors of 73008 that divides 72996 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 169, 208, 216, 234, 312, 338, 351, 432, 468, 507, 624, 676, 702, 936, 1014, 1352, 1404, 1521, 1872, 2028, 2704, 2808, 3042, 4056, 4563, 5616, 6084, 8112, 9126, 12168, 18252, 24336, 36504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72996 and 73008. The biggest common factor number is the GCF number.
So the greatest common factor 72996 and 73008 is 12.

Also check out the Least Common Multiple of 72996 and 73008