What is the Greatest Common Factor of 630 and 650?

Greatest common factor (GCF) of 630 and 650 is 10.

GCF(630,650) = 10

We will now calculate the prime factors of 630 and 650, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 630 and 650.

How to find the GCF of 630 and 650?

We will first find the prime factorization of 630 and 650. After we will calculate the factors of 630 and 650 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 650

Prime factors of 650 are 2, 5, 13. Prime factorization of 650 in exponential form is:

650 = 2¹ × 5² × 13¹

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 650

List of positive integer factors of 650 that divides 630 without a remainder.

1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 630 and 650. The biggest common factor number is the GCF number.
So the greatest common factor 630 and 650 is 10.

Also check out the Least Common Multiple of 630 and 650