What is the Greatest Common Factor of 74240 and 74256?

Greatest common factor (GCF) of 74240 and 74256 is 16.

GCF(74240,74256) = 16

We will now calculate the prime factors of 74240 and 74256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74240 and 74256.

How to find the GCF of 74240 and 74256?

We will first find the prime factorization of 74240 and 74256. After we will calculate the factors of 74240 and 74256 and find the biggest common factor number .

Step-1: Prime Factorization of 74240

Prime factors of 74240 are 2, 5, 29. Prime factorization of 74240 in exponential form is:

74240 = 2⁹ × 5¹ × 29¹

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 74240

List of positive integer factors of 74240 that divides 74240 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 29, 32, 40, 58, 64, 80, 116, 128, 145, 160, 232, 256, 290, 320, 464, 512, 580, 640, 928, 1160, 1280, 1856, 2320, 2560, 3712, 4640, 7424, 9280, 14848, 18560, 37120

Step-4: Factors of 74256

List of positive integer factors of 74256 that divides 74240 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 74240 and 74256. The biggest common factor number is the GCF number.
So the greatest common factor 74240 and 74256 is 16.

Also check out the Least Common Multiple of 74240 and 74256