What is the Greatest Common Factor of 10635 and 10650?

Greatest common factor (GCF) of 10635 and 10650 is 15.

GCF(10635,10650) = 15

We will now calculate the prime factors of 10635 and 10650, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10635 and 10650.

How to find the GCF of 10635 and 10650?

We will first find the prime factorization of 10635 and 10650. After we will calculate the factors of 10635 and 10650 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10650

Prime factors of 10650 are 2, 3, 5, 71. Prime factorization of 10650 in exponential form is:

10650 = 2¹ × 3¹ × 5² × 71¹

Step-3: Factors of 10635

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

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

Step-4: Factors of 10650

List of positive integer factors of 10650 that divides 10635 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 71, 75, 142, 150, 213, 355, 426, 710, 1065, 1775, 2130, 3550, 5325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10635 and 10650. The biggest common factor number is the GCF number.
So the greatest common factor 10635 and 10650 is 15.

Also check out the Least Common Multiple of 10635 and 10650