What is the Greatest Common Factor of 36896 and 36900?

Greatest common factor (GCF) of 36896 and 36900 is 4.

GCF(36896,36900) = 4

We will now calculate the prime factors of 36896 and 36900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36896 and 36900.

How to find the GCF of 36896 and 36900?

We will first find the prime factorization of 36896 and 36900. After we will calculate the factors of 36896 and 36900 and find the biggest common factor number .

Step-1: Prime Factorization of 36896

Prime factors of 36896 are 2, 1153. Prime factorization of 36896 in exponential form is:

36896 = 2⁵ × 1153¹

Step-2: 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-3: Factors of 36896

List of positive integer factors of 36896 that divides 36896 without a remainder.

1, 2, 4, 8, 16, 32, 1153, 2306, 4612, 9224, 18448

Step-4: Factors of 36900

List of positive integer factors of 36900 that divides 36896 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36896 and 36900. The biggest common factor number is the GCF number.
So the greatest common factor 36896 and 36900 is 4.

Also check out the Least Common Multiple of 36896 and 36900