What is the Greatest Common Factor of 27256 and 27264?

Greatest common factor (GCF) of 27256 and 27264 is 8.

GCF(27256,27264) = 8

We will now calculate the prime factors of 27256 and 27264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27256 and 27264.

How to find the GCF of 27256 and 27264?

We will first find the prime factorization of 27256 and 27264. After we will calculate the factors of 27256 and 27264 and find the biggest common factor number .

Step-1: Prime Factorization of 27256

Prime factors of 27256 are 2, 3407. Prime factorization of 27256 in exponential form is:

27256 = 2³ × 3407¹

Step-2: Prime Factorization of 27264

Prime factors of 27264 are 2, 3, 71. Prime factorization of 27264 in exponential form is:

27264 = 2⁷ × 3¹ × 71¹

Step-3: Factors of 27256

List of positive integer factors of 27256 that divides 27256 without a remainder.

1, 2, 4, 8, 3407, 6814, 13628

Step-4: Factors of 27264

List of positive integer factors of 27264 that divides 27256 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 128, 142, 192, 213, 284, 384, 426, 568, 852, 1136, 1704, 2272, 3408, 4544, 6816, 9088, 13632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27256 and 27264. The biggest common factor number is the GCF number.
So the greatest common factor 27256 and 27264 is 8.

Also check out the Least Common Multiple of 27256 and 27264