What is the Greatest Common Factor of 34641 and 34656?

Greatest common factor (GCF) of 34641 and 34656 is 3.

GCF(34641,34656) = 3

We will now calculate the prime factors of 34641 and 34656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34641 and 34656.

How to find the GCF of 34641 and 34656?

We will first find the prime factorization of 34641 and 34656. After we will calculate the factors of 34641 and 34656 and find the biggest common factor number .

Step-1: Prime Factorization of 34641

Prime factors of 34641 are 3, 1283. Prime factorization of 34641 in exponential form is:

34641 = 3³ × 1283¹

Step-2: Prime Factorization of 34656

Prime factors of 34656 are 2, 3, 19. Prime factorization of 34656 in exponential form is:

34656 = 2⁵ × 3¹ × 19²

Step-3: Factors of 34641

List of positive integer factors of 34641 that divides 34641 without a remainder.

1, 3, 9, 27, 1283, 3849, 11547

Step-4: Factors of 34656

List of positive integer factors of 34656 that divides 34641 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 361, 456, 608, 722, 912, 1083, 1444, 1824, 2166, 2888, 4332, 5776, 8664, 11552, 17328

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34641 and 34656. The biggest common factor number is the GCF number.
So the greatest common factor 34641 and 34656 is 3.

Also check out the Least Common Multiple of 34641 and 34656