What is the Greatest Common Factor of 17664 and 17678?

Greatest common factor (GCF) of 17664 and 17678 is 2.

GCF(17664,17678) = 2

We will now calculate the prime factors of 17664 and 17678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17664 and 17678.

How to find the GCF of 17664 and 17678?

We will first find the prime factorization of 17664 and 17678. After we will calculate the factors of 17664 and 17678 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17678

Prime factors of 17678 are 2, 8839. Prime factorization of 17678 in exponential form is:

17678 = 2¹ × 8839¹

Step-3: Factors of 17664

List of positive integer factors of 17664 that divides 17664 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

Step-4: Factors of 17678

List of positive integer factors of 17678 that divides 17664 without a remainder.

1, 2, 8839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17664 and 17678. The biggest common factor number is the GCF number.
So the greatest common factor 17664 and 17678 is 2.

Also check out the Least Common Multiple of 17664 and 17678