What is the Greatest Common Factor of 623 and 630?

Greatest common factor (GCF) of 623 and 630 is 7.

GCF(623,630) = 7

We will now calculate the prime factors of 623 and 630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 623 and 630.

How to find the GCF of 623 and 630?

We will first find the prime factorization of 623 and 630. After we will calculate the factors of 623 and 630 and find the biggest common factor number .

Step-1: Prime Factorization of 623

Prime factors of 623 are 7, 89. Prime factorization of 623 in exponential form is:

623 = 7¹ × 89¹

Step-2: 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-3: Factors of 623

List of positive integer factors of 623 that divides 623 without a remainder.

1, 7, 89

Step-4: Factors of 630

List of positive integer factors of 630 that divides 623 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 623 and 630. The biggest common factor number is the GCF number.
So the greatest common factor 623 and 630 is 7.

Also check out the Least Common Multiple of 623 and 630