What is the Greatest Common Factor of 45180 and 45200?

Greatest common factor (GCF) of 45180 and 45200 is 20.

GCF(45180,45200) = 20

We will now calculate the prime factors of 45180 and 45200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45180 and 45200.

How to find the GCF of 45180 and 45200?

We will first find the prime factorization of 45180 and 45200. After we will calculate the factors of 45180 and 45200 and find the biggest common factor number .

Step-1: Prime Factorization of 45180

Prime factors of 45180 are 2, 3, 5, 251. Prime factorization of 45180 in exponential form is:

45180 = 2² × 3² × 5¹ × 251¹

Step-2: Prime Factorization of 45200

Prime factors of 45200 are 2, 5, 113. Prime factorization of 45200 in exponential form is:

45200 = 2⁴ × 5² × 113¹

Step-3: Factors of 45180

List of positive integer factors of 45180 that divides 45180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 251, 502, 753, 1004, 1255, 1506, 2259, 2510, 3012, 3765, 4518, 5020, 7530, 9036, 11295, 15060, 22590

Step-4: Factors of 45200

List of positive integer factors of 45200 that divides 45180 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 113, 200, 226, 400, 452, 565, 904, 1130, 1808, 2260, 2825, 4520, 5650, 9040, 11300, 22600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45180 and 45200. The biggest common factor number is the GCF number.
So the greatest common factor 45180 and 45200 is 20.

Also check out the Least Common Multiple of 45180 and 45200