What is the Greatest Common Factor of 630 and 636?

Greatest common factor (GCF) of 630 and 636 is 6.

GCF(630,636) = 6

We will now calculate the prime factors of 630 and 636, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 630 and 636.

How to find the GCF of 630 and 636?

We will first find the prime factorization of 630 and 636. After we will calculate the factors of 630 and 636 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 636

Prime factors of 636 are 2, 3, 53. Prime factorization of 636 in exponential form is:

636 = 2² × 3¹ × 53¹

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 636

List of positive integer factors of 636 that divides 630 without a remainder.

1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 630 and 636. The biggest common factor number is the GCF number.
So the greatest common factor 630 and 636 is 6.

Also check out the Least Common Multiple of 630 and 636