What is the Greatest Common Factor of 65625 and 65632?

Greatest common factor (GCF) of 65625 and 65632 is 7.

GCF(65625,65632) = 7

We will now calculate the prime factors of 65625 and 65632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65625 and 65632.

How to find the GCF of 65625 and 65632?

We will first find the prime factorization of 65625 and 65632. After we will calculate the factors of 65625 and 65632 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 65632

Prime factors of 65632 are 2, 7, 293. Prime factorization of 65632 in exponential form is:

65632 = 2⁵ × 7¹ × 293¹

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 65632

List of positive integer factors of 65632 that divides 65625 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 293, 586, 1172, 2051, 2344, 4102, 4688, 8204, 9376, 16408, 32816

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65625 and 65632. The biggest common factor number is the GCF number.
So the greatest common factor 65625 and 65632 is 7.

Also check out the Least Common Multiple of 65625 and 65632