What is the Greatest Common Factor of 45200 and 45209?

Greatest common factor (GCF) of 45200 and 45209 is 1.

GCF(45200,45209) = 1

We will now calculate the prime factors of 45200 and 45209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45200 and 45209.

How to find the GCF of 45200 and 45209?

We will first find the prime factorization of 45200 and 45209. After we will calculate the factors of 45200 and 45209 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 45209

Prime factors of 45209 are 53, 853. Prime factorization of 45209 in exponential form is:

45209 = 53¹ × 853¹

Step-3: Factors of 45200

List of positive integer factors of 45200 that divides 45200 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

Step-4: Factors of 45209

List of positive integer factors of 45209 that divides 45200 without a remainder.

1, 53, 853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45200 and 45209. The biggest common factor number is the GCF number.
So the greatest common factor 45200 and 45209 is 1.

Also check out the Least Common Multiple of 45200 and 45209