What is the Greatest Common Factor of 36200 and 36210?

Greatest common factor (GCF) of 36200 and 36210 is 10.

GCF(36200,36210) = 10

We will now calculate the prime factors of 36200 and 36210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36200 and 36210.

How to find the GCF of 36200 and 36210?

We will first find the prime factorization of 36200 and 36210. After we will calculate the factors of 36200 and 36210 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 36210

Prime factors of 36210 are 2, 3, 5, 17, 71. Prime factorization of 36210 in exponential form is:

36210 = 2¹ × 3¹ × 5¹ × 17¹ × 71¹

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 36210

List of positive integer factors of 36210 that divides 36200 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 71, 85, 102, 142, 170, 213, 255, 355, 426, 510, 710, 1065, 1207, 2130, 2414, 3621, 6035, 7242, 12070, 18105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36200 and 36210. The biggest common factor number is the GCF number.
So the greatest common factor 36200 and 36210 is 10.

Also check out the Least Common Multiple of 36200 and 36210