What is the Greatest Common Factor of 36900 and 36912?

Greatest common factor (GCF) of 36900 and 36912 is 12.

GCF(36900,36912) = 12

We will now calculate the prime factors of 36900 and 36912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36900 and 36912.

How to find the GCF of 36900 and 36912?

We will first find the prime factorization of 36900 and 36912. After we will calculate the factors of 36900 and 36912 and find the biggest common factor number .

Step-1: Prime Factorization of 36900

Prime factors of 36900 are 2, 3, 5, 41. Prime factorization of 36900 in exponential form is:

36900 = 2² × 3² × 5² × 41¹

Step-2: Prime Factorization of 36912

Prime factors of 36912 are 2, 3, 769. Prime factorization of 36912 in exponential form is:

36912 = 2⁴ × 3¹ × 769¹

Step-3: Factors of 36900

List of positive integer factors of 36900 that divides 36900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 41, 45, 50, 60, 75, 82, 90, 100, 123, 150, 164, 180, 205, 225, 246, 300, 369, 410, 450, 492, 615, 738, 820, 900, 1025, 1230, 1476, 1845, 2050, 2460, 3075, 3690, 4100, 6150, 7380, 9225, 12300, 18450

Step-4: Factors of 36912

List of positive integer factors of 36912 that divides 36900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 769, 1538, 2307, 3076, 4614, 6152, 9228, 12304, 18456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36900 and 36912. The biggest common factor number is the GCF number.
So the greatest common factor 36900 and 36912 is 12.

Also check out the Least Common Multiple of 36900 and 36912