What is the Greatest Common Factor of 900 and 917?

Greatest common factor (GCF) of 900 and 917 is 1.

GCF(900,917) = 1

We will now calculate the prime factors of 900 and 917, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 917.

How to find the GCF of 900 and 917?

We will first find the prime factorization of 900 and 917. After we will calculate the factors of 900 and 917 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 917

Prime factors of 917 are 7, 131. Prime factorization of 917 in exponential form is:

917 = 7¹ × 131¹

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 917

List of positive integer factors of 917 that divides 900 without a remainder.

1, 7, 131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 917. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 917 is 1.

Also check out the Least Common Multiple of 900 and 917