What is the Greatest Common Factor of 65625 and 65637?

Greatest common factor (GCF) of 65625 and 65637 is 3.

GCF(65625,65637) = 3

We will now calculate the prime factors of 65625 and 65637, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65625 and 65637.

How to find the GCF of 65625 and 65637?

We will first find the prime factorization of 65625 and 65637. After we will calculate the factors of 65625 and 65637 and find the biggest common factor number .

Step-1: Prime Factorization of 65625

Prime factors of 65625 are 3, 5, 7. Prime factorization of 65625 in exponential form is:

65625 = 3¹ × 5⁵ × 7¹

Step-2: Prime Factorization of 65637

Prime factors of 65637 are 3, 11, 13, 17. Prime factorization of 65637 in exponential form is:

65637 = 3³ × 11¹ × 13¹ × 17¹

Step-3: Factors of 65625

List of positive integer factors of 65625 that divides 65625 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875, 1875, 2625, 3125, 4375, 9375, 13125, 21875

Step-4: Factors of 65637

List of positive integer factors of 65637 that divides 65625 without a remainder.

1, 3, 9, 11, 13, 17, 27, 33, 39, 51, 99, 117, 143, 153, 187, 221, 297, 351, 429, 459, 561, 663, 1287, 1683, 1989, 2431, 3861, 5049, 5967, 7293, 21879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65625 and 65637. The biggest common factor number is the GCF number.
So the greatest common factor 65625 and 65637 is 3.

Also check out the Least Common Multiple of 65625 and 65637