What is the Greatest Common Factor of 65625 and 65640?

Greatest common factor (GCF) of 65625 and 65640 is 15.

GCF(65625,65640) = 15

We will now calculate the prime factors of 65625 and 65640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65625 and 65640.

How to find the GCF of 65625 and 65640?

We will first find the prime factorization of 65625 and 65640. After we will calculate the factors of 65625 and 65640 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 65640

Prime factors of 65640 are 2, 3, 5, 547. Prime factorization of 65640 in exponential form is:

65640 = 2³ × 3¹ × 5¹ × 547¹

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 65640

List of positive integer factors of 65640 that divides 65625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 547, 1094, 1641, 2188, 2735, 3282, 4376, 5470, 6564, 8205, 10940, 13128, 16410, 21880, 32820

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65625 and 65640. The biggest common factor number is the GCF number.
So the greatest common factor 65625 and 65640 is 15.

Also check out the Least Common Multiple of 65625 and 65640