What is the Greatest Common Factor of 74256 and 74262?

Greatest common factor (GCF) of 74256 and 74262 is 6.

GCF(74256,74262) = 6

We will now calculate the prime factors of 74256 and 74262, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74256 and 74262.

How to find the GCF of 74256 and 74262?

We will first find the prime factorization of 74256 and 74262. After we will calculate the factors of 74256 and 74262 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 74262

Prime factors of 74262 are 2, 3, 12377. Prime factorization of 74262 in exponential form is:

74262 = 2¹ × 3¹ × 12377¹

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 74262

List of positive integer factors of 74262 that divides 74256 without a remainder.

1, 2, 3, 6, 12377, 24754, 37131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74256 and 74262. The biggest common factor number is the GCF number.
So the greatest common factor 74256 and 74262 is 6.

Also check out the Least Common Multiple of 74256 and 74262