What is the Greatest Common Factor of 74241 and 74256?

Greatest common factor (GCF) of 74241 and 74256 is 3.

GCF(74241,74256) = 3

We will now calculate the prime factors of 74241 and 74256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74241 and 74256.

How to find the GCF of 74241 and 74256?

We will first find the prime factorization of 74241 and 74256. After we will calculate the factors of 74241 and 74256 and find the biggest common factor number .

Step-1: Prime Factorization of 74241

Prime factors of 74241 are 3, 73, 113. Prime factorization of 74241 in exponential form is:

74241 = 3² × 73¹ × 113¹

Step-2: 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-3: Factors of 74241

List of positive integer factors of 74241 that divides 74241 without a remainder.

1, 3, 9, 73, 113, 219, 339, 657, 1017, 8249, 24747

Step-4: Factors of 74256

List of positive integer factors of 74256 that divides 74241 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74241 and 74256. The biggest common factor number is the GCF number.
So the greatest common factor 74241 and 74256 is 3.

Also check out the Least Common Multiple of 74241 and 74256