What is the Greatest Common Factor of 74256 and 74264?

Greatest common factor (GCF) of 74256 and 74264 is 8.

GCF(74256,74264) = 8

We will now calculate the prime factors of 74256 and 74264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74256 and 74264.

How to find the GCF of 74256 and 74264?

We will first find the prime factorization of 74256 and 74264. After we will calculate the factors of 74256 and 74264 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 74264

Prime factors of 74264 are 2, 9283. Prime factorization of 74264 in exponential form is:

74264 = 2³ × 9283¹

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 74264

List of positive integer factors of 74264 that divides 74256 without a remainder.

1, 2, 4, 8, 9283, 18566, 37132

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74256 and 74264. The biggest common factor number is the GCF number.
So the greatest common factor 74256 and 74264 is 8.

Also check out the Least Common Multiple of 74256 and 74264