What is the Greatest Common Factor of 6174 and 6188?

Greatest common factor (GCF) of 6174 and 6188 is 14.

GCF(6174,6188) = 14

We will now calculate the prime factors of 6174 and 6188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6174 and 6188.

How to find the GCF of 6174 and 6188?

We will first find the prime factorization of 6174 and 6188. After we will calculate the factors of 6174 and 6188 and find the biggest common factor number .

Step-1: Prime Factorization of 6174

Prime factors of 6174 are 2, 3, 7. Prime factorization of 6174 in exponential form is:

6174 = 2¹ × 3² × 7³

Step-2: Prime Factorization of 6188

Prime factors of 6188 are 2, 7, 13, 17. Prime factorization of 6188 in exponential form is:

6188 = 2² × 7¹ × 13¹ × 17¹

Step-3: Factors of 6174

List of positive integer factors of 6174 that divides 6174 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087

Step-4: Factors of 6188

List of positive integer factors of 6188 that divides 6174 without a remainder.

1, 2, 4, 7, 13, 14, 17, 26, 28, 34, 52, 68, 91, 119, 182, 221, 238, 364, 442, 476, 884, 1547, 3094

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6174 and 6188. The biggest common factor number is the GCF number.
So the greatest common factor 6174 and 6188 is 14.

Also check out the Least Common Multiple of 6174 and 6188