What is the Greatest Common Factor of 900 and 914?

Greatest common factor (GCF) of 900 and 914 is 2.

GCF(900,914) = 2

We will now calculate the prime factors of 900 and 914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 900 and 914.

How to find the GCF of 900 and 914?

We will first find the prime factorization of 900 and 914. After we will calculate the factors of 900 and 914 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 914

Prime factors of 914 are 2, 457. Prime factorization of 914 in exponential form is:

914 = 2¹ × 457¹

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 914

List of positive integer factors of 914 that divides 900 without a remainder.

1, 2, 457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 900 and 914. The biggest common factor number is the GCF number.
So the greatest common factor 900 and 914 is 2.

Also check out the Least Common Multiple of 900 and 914