What is the Greatest Common Factor of 65664 and 65682?

Greatest common factor (GCF) of 65664 and 65682 is 18.

GCF(65664,65682) = 18

We will now calculate the prime factors of 65664 and 65682, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65664 and 65682.

How to find the GCF of 65664 and 65682?

We will first find the prime factorization of 65664 and 65682. After we will calculate the factors of 65664 and 65682 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 65682

Prime factors of 65682 are 2, 3, 41, 89. Prime factorization of 65682 in exponential form is:

65682 = 2¹ × 3² × 41¹ × 89¹

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 65682

List of positive integer factors of 65682 that divides 65664 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 89, 123, 178, 246, 267, 369, 534, 738, 801, 1602, 3649, 7298, 10947, 21894, 32841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65664 and 65682. The biggest common factor number is the GCF number.
So the greatest common factor 65664 and 65682 is 18.

Also check out the Least Common Multiple of 65664 and 65682