What is the Greatest Common Factor of 5174 and 5180?

Greatest common factor (GCF) of 5174 and 5180 is 2.

GCF(5174,5180) = 2

We will now calculate the prime factors of 5174 and 5180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5174 and 5180.

How to find the GCF of 5174 and 5180?

We will first find the prime factorization of 5174 and 5180. After we will calculate the factors of 5174 and 5180 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 5180

Prime factors of 5180 are 2, 5, 7, 37. Prime factorization of 5180 in exponential form is:

5180 = 2² × 5¹ × 7¹ × 37¹

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 5180

List of positive integer factors of 5180 that divides 5174 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 37, 70, 74, 140, 148, 185, 259, 370, 518, 740, 1036, 1295, 2590

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5174 and 5180. The biggest common factor number is the GCF number.
So the greatest common factor 5174 and 5180 is 2.

Also check out the Least Common Multiple of 5174 and 5180