What is the Greatest Common Factor of 38256 and 38272?

Greatest common factor (GCF) of 38256 and 38272 is 16.

GCF(38256,38272) = 16

We will now calculate the prime factors of 38256 and 38272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38256 and 38272.

How to find the GCF of 38256 and 38272?

We will first find the prime factorization of 38256 and 38272. After we will calculate the factors of 38256 and 38272 and find the biggest common factor number .

Step-1: Prime Factorization of 38256

Prime factors of 38256 are 2, 3, 797. Prime factorization of 38256 in exponential form is:

38256 = 2⁴ × 3¹ × 797¹

Step-2: Prime Factorization of 38272

Prime factors of 38272 are 2, 13, 23. Prime factorization of 38272 in exponential form is:

38272 = 2⁷ × 13¹ × 23¹

Step-3: Factors of 38256

List of positive integer factors of 38256 that divides 38256 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 797, 1594, 2391, 3188, 4782, 6376, 9564, 12752, 19128

Step-4: Factors of 38272

List of positive integer factors of 38272 that divides 38256 without a remainder.

1, 2, 4, 8, 13, 16, 23, 26, 32, 46, 52, 64, 92, 104, 128, 184, 208, 299, 368, 416, 598, 736, 832, 1196, 1472, 1664, 2392, 2944, 4784, 9568, 19136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38256 and 38272. The biggest common factor number is the GCF number.
So the greatest common factor 38256 and 38272 is 16.

Also check out the Least Common Multiple of 38256 and 38272