What is the Greatest Common Factor of 5187 and 5200?

Greatest common factor (GCF) of 5187 and 5200 is 13.

GCF(5187,5200) = 13

We will now calculate the prime factors of 5187 and 5200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5187 and 5200.

How to find the GCF of 5187 and 5200?

We will first find the prime factorization of 5187 and 5200. After we will calculate the factors of 5187 and 5200 and find the biggest common factor number .

Step-1: Prime Factorization of 5187

Prime factors of 5187 are 3, 7, 13, 19. Prime factorization of 5187 in exponential form is:

5187 = 3¹ × 7¹ × 13¹ × 19¹

Step-2: Prime Factorization of 5200

Prime factors of 5200 are 2, 5, 13. Prime factorization of 5200 in exponential form is:

5200 = 2⁴ × 5² × 13¹

Step-3: Factors of 5187

List of positive integer factors of 5187 that divides 5187 without a remainder.

1, 3, 7, 13, 19, 21, 39, 57, 91, 133, 247, 273, 399, 741, 1729

Step-4: Factors of 5200

List of positive integer factors of 5200 that divides 5187 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5187 and 5200. The biggest common factor number is the GCF number.
So the greatest common factor 5187 and 5200 is 13.

Also check out the Least Common Multiple of 5187 and 5200