What is the Greatest Common Factor of 74238 and 74256?

Greatest common factor (GCF) of 74238 and 74256 is 6.

GCF(74238,74256) = 6

We will now calculate the prime factors of 74238 and 74256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74238 and 74256.

How to find the GCF of 74238 and 74256?

We will first find the prime factorization of 74238 and 74256. After we will calculate the factors of 74238 and 74256 and find the biggest common factor number .

Step-1: Prime Factorization of 74238

Prime factors of 74238 are 2, 3, 12373. Prime factorization of 74238 in exponential form is:

74238 = 2¹ × 3¹ × 12373¹

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 74238

List of positive integer factors of 74238 that divides 74238 without a remainder.

1, 2, 3, 6, 12373, 24746, 37119

Step-4: Factors of 74256

List of positive integer factors of 74256 that divides 74238 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 74238 and 74256. The biggest common factor number is the GCF number.
So the greatest common factor 74238 and 74256 is 6.

Also check out the Least Common Multiple of 74238 and 74256