What is the Greatest Common Factor of 900 and 920?

Greatest common factor (GCF) of 900 and 920 is 20.

GCF(900,920) = 20

We will now calculate the prime factors of 900 and 920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 920.

How to find the GCF of 900 and 920?

We will first find the prime factorization of 900 and 920. After we will calculate the factors of 900 and 920 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 920

Prime factors of 920 are 2, 5, 23. Prime factorization of 920 in exponential form is:

920 = 2³ × 5¹ × 23¹

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 920

List of positive integer factors of 920 that divides 900 without a remainder.

1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 920. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 920 is 20.

Also check out the Least Common Multiple of 900 and 920