What is the Greatest Common Factor of 5174 and 5187?

Greatest common factor (GCF) of 5174 and 5187 is 13.

GCF(5174,5187) = 13

We will now calculate the prime factors of 5174 and 5187, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5174 and 5187.

How to find the GCF of 5174 and 5187?

We will first find the prime factorization of 5174 and 5187. After we will calculate the factors of 5174 and 5187 and find the biggest common factor number .

Step-1: Prime Factorization of 5174

Prime factors of 5174 are 2, 13, 199. Prime factorization of 5174 in exponential form is:

5174 = 2¹ × 13¹ × 199¹

Step-2: 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-3: Factors of 5174

List of positive integer factors of 5174 that divides 5174 without a remainder.

1, 2, 13, 26, 199, 398, 2587

Step-4: Factors of 5187

List of positive integer factors of 5187 that divides 5174 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5174 and 5187. The biggest common factor number is the GCF number.
So the greatest common factor 5174 and 5187 is 13.

Also check out the Least Common Multiple of 5174 and 5187