What is the Greatest Common Factor of 10625 and 10635?

Greatest common factor (GCF) of 10625 and 10635 is 5.

GCF(10625,10635) = 5

We will now calculate the prime factors of 10625 and 10635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10625 and 10635.

How to find the GCF of 10625 and 10635?

We will first find the prime factorization of 10625 and 10635. After we will calculate the factors of 10625 and 10635 and find the biggest common factor number .

Step-1: Prime Factorization of 10625

Prime factors of 10625 are 5, 17. Prime factorization of 10625 in exponential form is:

10625 = 5⁴ × 17¹

Step-2: Prime Factorization of 10635

Prime factors of 10635 are 3, 5, 709. Prime factorization of 10635 in exponential form is:

10635 = 3¹ × 5¹ × 709¹

Step-3: Factors of 10625

List of positive integer factors of 10625 that divides 10625 without a remainder.

1, 5, 17, 25, 85, 125, 425, 625, 2125

Step-4: Factors of 10635

List of positive integer factors of 10635 that divides 10625 without a remainder.

1, 3, 5, 15, 709, 2127, 3545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10625 and 10635. The biggest common factor number is the GCF number.
So the greatest common factor 10625 and 10635 is 5.

Also check out the Least Common Multiple of 10625 and 10635