What is the Greatest Common Factor of 630 and 635?

Greatest common factor (GCF) of 630 and 635 is 5.

GCF(630,635) = 5

We will now calculate the prime factors of 630 and 635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 630 and 635.

How to find the GCF of 630 and 635?

We will first find the prime factorization of 630 and 635. After we will calculate the factors of 630 and 635 and find the biggest common factor number .

Step-1: Prime Factorization of 630

Prime factors of 630 are 2, 3, 5, 7. Prime factorization of 630 in exponential form is:

630 = 2¹ × 3² × 5¹ × 7¹

Step-2: Prime Factorization of 635

Prime factors of 635 are 5, 127. Prime factorization of 635 in exponential form is:

635 = 5¹ × 127¹

Step-3: Factors of 630

List of positive integer factors of 630 that divides 630 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315

Step-4: Factors of 635

List of positive integer factors of 635 that divides 630 without a remainder.

1, 5, 127

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 630 and 635. The biggest common factor number is the GCF number.
So the greatest common factor 630 and 635 is 5.

Also check out the Least Common Multiple of 630 and 635