What is the Greatest Common Factor of 65664 and 65680?

Greatest common factor (GCF) of 65664 and 65680 is 16.

GCF(65664,65680) = 16

We will now calculate the prime factors of 65664 and 65680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65664 and 65680.

How to find the GCF of 65664 and 65680?

We will first find the prime factorization of 65664 and 65680. After we will calculate the factors of 65664 and 65680 and find the biggest common factor number .

Step-1: Prime Factorization of 65664

Prime factors of 65664 are 2, 3, 19. Prime factorization of 65664 in exponential form is:

65664 = 2⁷ × 3³ × 19¹

Step-2: Prime Factorization of 65680

Prime factors of 65680 are 2, 5, 821. Prime factorization of 65680 in exponential form is:

65680 = 2⁴ × 5¹ × 821¹

Step-3: Factors of 65664

List of positive integer factors of 65664 that divides 65664 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 64, 72, 76, 96, 108, 114, 128, 144, 152, 171, 192, 216, 228, 288, 304, 342, 384, 432, 456, 513, 576, 608, 684, 864, 912, 1026, 1152, 1216, 1368, 1728, 1824, 2052, 2432, 2736, 3456, 3648, 4104, 5472, 7296, 8208, 10944, 16416, 21888, 32832

Step-4: Factors of 65680

List of positive integer factors of 65680 that divides 65664 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 821, 1642, 3284, 4105, 6568, 8210, 13136, 16420, 32840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65664 and 65680. The biggest common factor number is the GCF number.
So the greatest common factor 65664 and 65680 is 16.

Also check out the Least Common Multiple of 65664 and 65680