What is the Greatest Common Factor of 17664 and 17671?

Greatest common factor (GCF) of 17664 and 17671 is 1.

GCF(17664,17671) = 1

We will now calculate the prime factors of 17664 and 17671, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17664 and 17671.

How to find the GCF of 17664 and 17671?

We will first find the prime factorization of 17664 and 17671. After we will calculate the factors of 17664 and 17671 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 17671

Prime factors of 17671 are 41, 431. Prime factorization of 17671 in exponential form is:

17671 = 41¹ × 431¹

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 17671

List of positive integer factors of 17671 that divides 17664 without a remainder.

1, 41, 431

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17664 and 17671. The biggest common factor number is the GCF number.
So the greatest common factor 17664 and 17671 is 1.

Also check out the Least Common Multiple of 17664 and 17671