What is the Greatest Common Factor of 74256 and 74268?

Greatest common factor (GCF) of 74256 and 74268 is 12.

GCF(74256,74268) = 12

We will now calculate the prime factors of 74256 and 74268, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74256 and 74268.

How to find the GCF of 74256 and 74268?

We will first find the prime factorization of 74256 and 74268. After we will calculate the factors of 74256 and 74268 and find the biggest common factor number .

Step-1: Prime Factorization of 74256

Prime factors of 74256 are 2, 3, 7, 13, 17. Prime factorization of 74256 in exponential form is:

74256 = 2⁴ × 3¹ × 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 74268

Prime factors of 74268 are 2, 3, 2063. Prime factorization of 74268 in exponential form is:

74268 = 2² × 3² × 2063¹

Step-3: Factors of 74256

List of positive integer factors of 74256 that divides 74256 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 17, 21, 24, 26, 28, 34, 39, 42, 48, 51, 52, 56, 68, 78, 84, 91, 102, 104, 112, 119, 136, 156, 168, 182, 204, 208, 221, 238, 272, 273, 312, 336, 357, 364, 408, 442, 476, 546, 624, 663, 714, 728, 816, 884, 952, 1092, 1326, 1428, 1456, 1547, 1768, 1904, 2184, 2652, 2856, 3094, 3536, 4368, 4641, 5304, 5712, 6188, 9282, 10608, 12376, 18564, 24752, 37128

Step-4: Factors of 74268

List of positive integer factors of 74268 that divides 74256 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2063, 4126, 6189, 8252, 12378, 18567, 24756, 37134

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74256 and 74268. The biggest common factor number is the GCF number.
So the greatest common factor 74256 and 74268 is 12.

Also check out the Least Common Multiple of 74256 and 74268