What is the Greatest Common Factor of 17664 and 17680?

Greatest common factor (GCF) of 17664 and 17680 is 16.

GCF(17664,17680) = 16

We will now calculate the prime factors of 17664 and 17680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17664 and 17680.

How to find the GCF of 17664 and 17680?

We will first find the prime factorization of 17664 and 17680. After we will calculate the factors of 17664 and 17680 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 17680

Prime factors of 17680 are 2, 5, 13, 17. Prime factorization of 17680 in exponential form is:

17680 = 2⁴ × 5¹ × 13¹ × 17¹

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 17680

List of positive integer factors of 17680 that divides 17664 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 26, 34, 40, 52, 65, 68, 80, 85, 104, 130, 136, 170, 208, 221, 260, 272, 340, 442, 520, 680, 884, 1040, 1105, 1360, 1768, 2210, 3536, 4420, 8840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17664 and 17680. The biggest common factor number is the GCF number.
So the greatest common factor 17664 and 17680 is 16.

Also check out the Least Common Multiple of 17664 and 17680