What is the Greatest Common Factor of 900 and 909?

Greatest common factor (GCF) of 900 and 909 is 9.

GCF(900,909) = 9

We will now calculate the prime factors of 900 and 909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 909.

How to find the GCF of 900 and 909?

We will first find the prime factorization of 900 and 909. After we will calculate the factors of 900 and 909 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 909

Prime factors of 909 are 3, 101. Prime factorization of 909 in exponential form is:

909 = 3² × 101¹

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 909

List of positive integer factors of 909 that divides 900 without a remainder.

1, 3, 9, 101, 303

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 909. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 909 is 9.

Also check out the Least Common Multiple of 900 and 909