What is the Greatest Common Factor of 630 and 644?

Greatest common factor (GCF) of 630 and 644 is 14.

GCF(630,644) = 14

We will now calculate the prime factors of 630 and 644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 630 and 644.

How to find the GCF of 630 and 644?

We will first find the prime factorization of 630 and 644. After we will calculate the factors of 630 and 644 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 644

Prime factors of 644 are 2, 7, 23. Prime factorization of 644 in exponential form is:

644 = 2² × 7¹ × 23¹

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 644

List of positive integer factors of 644 that divides 630 without a remainder.

1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 630 and 644. The biggest common factor number is the GCF number.
So the greatest common factor 630 and 644 is 14.

Also check out the Least Common Multiple of 630 and 644