What is the Greatest Common Factor of 36200 and 36208?

Greatest common factor (GCF) of 36200 and 36208 is 8.

GCF(36200,36208) = 8

We will now calculate the prime factors of 36200 and 36208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36200 and 36208.

How to find the GCF of 36200 and 36208?

We will first find the prime factorization of 36200 and 36208. After we will calculate the factors of 36200 and 36208 and find the biggest common factor number .

Step-1: Prime Factorization of 36200

Prime factors of 36200 are 2, 5, 181. Prime factorization of 36200 in exponential form is:

36200 = 2³ × 5² × 181¹

Step-2: Prime Factorization of 36208

Prime factors of 36208 are 2, 31, 73. Prime factorization of 36208 in exponential form is:

36208 = 2⁴ × 31¹ × 73¹

Step-3: Factors of 36200

List of positive integer factors of 36200 that divides 36200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 181, 200, 362, 724, 905, 1448, 1810, 3620, 4525, 7240, 9050, 18100

Step-4: Factors of 36208

List of positive integer factors of 36208 that divides 36200 without a remainder.

1, 2, 4, 8, 16, 31, 62, 73, 124, 146, 248, 292, 496, 584, 1168, 2263, 4526, 9052, 18104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36200 and 36208. The biggest common factor number is the GCF number.
So the greatest common factor 36200 and 36208 is 8.

Also check out the Least Common Multiple of 36200 and 36208