What is the Greatest Common Factor of 37107 and 37114?

Greatest common factor (GCF) of 37107 and 37114 is 7.

GCF(37107,37114) = 7

We will now calculate the prime factors of 37107 and 37114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37107 and 37114.

How to find the GCF of 37107 and 37114?

We will first find the prime factorization of 37107 and 37114. After we will calculate the factors of 37107 and 37114 and find the biggest common factor number .

Step-1: Prime Factorization of 37107

Prime factors of 37107 are 3, 7, 19, 31. Prime factorization of 37107 in exponential form is:

37107 = 3² × 7¹ × 19¹ × 31¹

Step-2: Prime Factorization of 37114

Prime factors of 37114 are 2, 7, 11, 241. Prime factorization of 37114 in exponential form is:

37114 = 2¹ × 7¹ × 11¹ × 241¹

Step-3: Factors of 37107

List of positive integer factors of 37107 that divides 37107 without a remainder.

1, 3, 7, 9, 19, 21, 31, 57, 63, 93, 133, 171, 217, 279, 399, 589, 651, 1197, 1767, 1953, 4123, 5301, 12369

Step-4: Factors of 37114

List of positive integer factors of 37114 that divides 37107 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 241, 482, 1687, 2651, 3374, 5302, 18557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37107 and 37114. The biggest common factor number is the GCF number.
So the greatest common factor 37107 and 37114 is 7.

Also check out the Least Common Multiple of 37107 and 37114