What is the Greatest Common Factor of 900 and 912?

Greatest common factor (GCF) of 900 and 912 is 12.

GCF(900,912) = 12

We will now calculate the prime factors of 900 and 912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 912.

How to find the GCF of 900 and 912?

We will first find the prime factorization of 900 and 912. After we will calculate the factors of 900 and 912 and find the biggest common factor number .

Step-1: Prime Factorization of 900

Prime factors of 900 are 2, 3, 5. Prime factorization of 900 in exponential form is:

900 = 2² × 3² × 5²

Step-2: Prime Factorization of 912

Prime factors of 912 are 2, 3, 19. Prime factorization of 912 in exponential form is:

912 = 2⁴ × 3¹ × 19¹

Step-3: Factors of 900

List of positive integer factors of 900 that divides 900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450

Step-4: Factors of 912

List of positive integer factors of 912 that divides 900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 912. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 912 is 12.

Also check out the Least Common Multiple of 900 and 912