What is the Greatest Common Factor of 624 and 633?

Greatest common factor (GCF) of 624 and 633 is 3.

GCF(624,633) = 3

We will now calculate the prime factors of 624 and 633, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 624 and 633.

How to find the GCF of 624 and 633?

We will first find the prime factorization of 624 and 633. After we will calculate the factors of 624 and 633 and find the biggest common factor number .

Step-1: Prime Factorization of 624

Prime factors of 624 are 2, 3, 13. Prime factorization of 624 in exponential form is:

624 = 2⁴ × 3¹ × 13¹

Step-2: Prime Factorization of 633

Prime factors of 633 are 3, 211. Prime factorization of 633 in exponential form is:

633 = 3¹ × 211¹

Step-3: Factors of 624

List of positive integer factors of 624 that divides 624 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312

Step-4: Factors of 633

List of positive integer factors of 633 that divides 624 without a remainder.

1, 3, 211

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 624 and 633. The biggest common factor number is the GCF number.
So the greatest common factor 624 and 633 is 3.

Also check out the Least Common Multiple of 624 and 633