What is the Greatest Common Factor of 900 and 915?

Greatest common factor (GCF) of 900 and 915 is 15.

GCF(900,915) = 15

We will now calculate the prime factors of 900 and 915, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 915.

How to find the GCF of 900 and 915?

We will first find the prime factorization of 900 and 915. After we will calculate the factors of 900 and 915 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 915

Prime factors of 915 are 3, 5, 61. Prime factorization of 915 in exponential form is:

915 = 3¹ × 5¹ × 61¹

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 915

List of positive integer factors of 915 that divides 900 without a remainder.

1, 3, 5, 15, 61, 183, 305

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 915. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 915 is 15.

Also check out the Least Common Multiple of 900 and 915