What is the Greatest Common Factor of 37109 and 37114?

Greatest common factor (GCF) of 37109 and 37114 is 1.

GCF(37109,37114) = 1

We will now calculate the prime factors of 37109 and 37114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37109 and 37114.

How to find the GCF of 37109 and 37114?

We will first find the prime factorization of 37109 and 37114. After we will calculate the factors of 37109 and 37114 and find the biggest common factor number .

Step-1: Prime Factorization of 37109

Prime factors of 37109 are 43, 863. Prime factorization of 37109 in exponential form is:

37109 = 43¹ × 863¹

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 37109

List of positive integer factors of 37109 that divides 37109 without a remainder.

1, 43, 863

Step-4: Factors of 37114

List of positive integer factors of 37114 that divides 37109 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 37109 and 37114. The biggest common factor number is the GCF number.
So the greatest common factor 37109 and 37114 is 1.

Also check out the Least Common Multiple of 37109 and 37114