What is the Greatest Common Factor of 13174 and 13188?

Greatest common factor (GCF) of 13174 and 13188 is 14.

GCF(13174,13188) = 14

We will now calculate the prime factors of 13174 and 13188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13174 and 13188.

How to find the GCF of 13174 and 13188?

We will first find the prime factorization of 13174 and 13188. After we will calculate the factors of 13174 and 13188 and find the biggest common factor number .

Step-1: Prime Factorization of 13174

Prime factors of 13174 are 2, 7, 941. Prime factorization of 13174 in exponential form is:

13174 = 2¹ × 7¹ × 941¹

Step-2: Prime Factorization of 13188

Prime factors of 13188 are 2, 3, 7, 157. Prime factorization of 13188 in exponential form is:

13188 = 2² × 3¹ × 7¹ × 157¹

Step-3: Factors of 13174

List of positive integer factors of 13174 that divides 13174 without a remainder.

1, 2, 7, 14, 941, 1882, 6587

Step-4: Factors of 13188

List of positive integer factors of 13188 that divides 13174 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 157, 314, 471, 628, 942, 1099, 1884, 2198, 3297, 4396, 6594

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13174 and 13188. The biggest common factor number is the GCF number.
So the greatest common factor 13174 and 13188 is 14.

Also check out the Least Common Multiple of 13174 and 13188