What is the Greatest Common Factor of 74256 and 74269?

Greatest common factor (GCF) of 74256 and 74269 is 13.

GCF(74256,74269) = 13

We will now calculate the prime factors of 74256 and 74269, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74256 and 74269.

How to find the GCF of 74256 and 74269?

We will first find the prime factorization of 74256 and 74269. After we will calculate the factors of 74256 and 74269 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 74269

Prime factors of 74269 are 13, 29, 197. Prime factorization of 74269 in exponential form is:

74269 = 13¹ × 29¹ × 197¹

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 74269

List of positive integer factors of 74269 that divides 74256 without a remainder.

1, 13, 29, 197, 377, 2561, 5713

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74256 and 74269. The biggest common factor number is the GCF number.
So the greatest common factor 74256 and 74269 is 13.

Also check out the Least Common Multiple of 74256 and 74269