What is the Greatest Common Factor of 630 and 634?

Greatest common factor (GCF) of 630 and 634 is 2.

GCF(630,634) = 2

We will now calculate the prime factors of 630 and 634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 630 and 634.

How to find the GCF of 630 and 634?

We will first find the prime factorization of 630 and 634. After we will calculate the factors of 630 and 634 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 634

Prime factors of 634 are 2, 317. Prime factorization of 634 in exponential form is:

634 = 2¹ × 317¹

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 634

List of positive integer factors of 634 that divides 630 without a remainder.

1, 2, 317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 630 and 634. The biggest common factor number is the GCF number.
So the greatest common factor 630 and 634 is 2.

Also check out the Least Common Multiple of 630 and 634