What is the Greatest Common Factor of 74256 and 74266?

Greatest common factor (GCF) of 74256 and 74266 is 2.

GCF(74256,74266) = 2

We will now calculate the prime factors of 74256 and 74266, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74256 and 74266.

How to find the GCF of 74256 and 74266?

We will first find the prime factorization of 74256 and 74266. After we will calculate the factors of 74256 and 74266 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 74266

Prime factors of 74266 are 2, 71, 523. Prime factorization of 74266 in exponential form is:

74266 = 2¹ × 71¹ × 523¹

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 74266

List of positive integer factors of 74266 that divides 74256 without a remainder.

1, 2, 71, 142, 523, 1046, 37133

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74256 and 74266. The biggest common factor number is the GCF number.
So the greatest common factor 74256 and 74266 is 2.

Also check out the Least Common Multiple of 74256 and 74266