What is the Greatest Common Factor of 65664 and 65684?

Greatest common factor (GCF) of 65664 and 65684 is 4.

GCF(65664,65684) = 4

We will now calculate the prime factors of 65664 and 65684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65664 and 65684.

How to find the GCF of 65664 and 65684?

We will first find the prime factorization of 65664 and 65684. After we will calculate the factors of 65664 and 65684 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 65684

Prime factors of 65684 are 2, 16421. Prime factorization of 65684 in exponential form is:

65684 = 2² × 16421¹

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 65684

List of positive integer factors of 65684 that divides 65664 without a remainder.

1, 2, 4, 16421, 32842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65664 and 65684. The biggest common factor number is the GCF number.
So the greatest common factor 65664 and 65684 is 4.

Also check out the Least Common Multiple of 65664 and 65684