What is the Greatest Common Factor of 17646 and 17664?

Greatest common factor (GCF) of 17646 and 17664 is 6.

GCF(17646,17664) = 6

We will now calculate the prime factors of 17646 and 17664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17646 and 17664.

How to find the GCF of 17646 and 17664?

We will first find the prime factorization of 17646 and 17664. After we will calculate the factors of 17646 and 17664 and find the biggest common factor number .

Step-1: Prime Factorization of 17646

Prime factors of 17646 are 2, 3, 17, 173. Prime factorization of 17646 in exponential form is:

17646 = 2¹ × 3¹ × 17¹ × 173¹

Step-2: Prime Factorization of 17664

Prime factors of 17664 are 2, 3, 23. Prime factorization of 17664 in exponential form is:

17664 = 2⁸ × 3¹ × 23¹

Step-3: Factors of 17646

List of positive integer factors of 17646 that divides 17646 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 173, 346, 519, 1038, 2941, 5882, 8823

Step-4: Factors of 17664

List of positive integer factors of 17664 that divides 17646 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 64, 69, 92, 96, 128, 138, 184, 192, 256, 276, 368, 384, 552, 736, 768, 1104, 1472, 2208, 2944, 4416, 5888, 8832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17646 and 17664. The biggest common factor number is the GCF number.
So the greatest common factor 17646 and 17664 is 6.

Also check out the Least Common Multiple of 17646 and 17664