What is the Greatest Common Factor of 65646 and 65664?

Greatest common factor (GCF) of 65646 and 65664 is 18.

GCF(65646,65664) = 18

We will now calculate the prime factors of 65646 and 65664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65646 and 65664.

How to find the GCF of 65646 and 65664?

We will first find the prime factorization of 65646 and 65664. After we will calculate the factors of 65646 and 65664 and find the biggest common factor number .

Step-1: Prime Factorization of 65646

Prime factors of 65646 are 2, 3, 7, 521. Prime factorization of 65646 in exponential form is:

65646 = 2¹ × 3² × 7¹ × 521¹

Step-2: 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-3: Factors of 65646

List of positive integer factors of 65646 that divides 65646 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 521, 1042, 1563, 3126, 3647, 4689, 7294, 9378, 10941, 21882, 32823

Step-4: Factors of 65664

List of positive integer factors of 65664 that divides 65646 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65646 and 65664. The biggest common factor number is the GCF number.
So the greatest common factor 65646 and 65664 is 18.

Also check out the Least Common Multiple of 65646 and 65664