What is the Greatest Common Factor of 37314 and 37319?

Greatest common factor (GCF) of 37314 and 37319 is 1.

GCF(37314,37319) = 1

We will now calculate the prime factors of 37314 and 37319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37314 and 37319.

How to find the GCF of 37314 and 37319?

We will first find the prime factorization of 37314 and 37319. After we will calculate the factors of 37314 and 37319 and find the biggest common factor number .

Step-1: Prime Factorization of 37314

Prime factors of 37314 are 2, 3, 691. Prime factorization of 37314 in exponential form is:

37314 = 2¹ × 3³ × 691¹

Step-2: Prime Factorization of 37319

Prime factors of 37319 are 67, 557. Prime factorization of 37319 in exponential form is:

37319 = 67¹ × 557¹

Step-3: Factors of 37314

List of positive integer factors of 37314 that divides 37314 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 691, 1382, 2073, 4146, 6219, 12438, 18657

Step-4: Factors of 37319

List of positive integer factors of 37319 that divides 37314 without a remainder.

1, 67, 557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37314 and 37319. The biggest common factor number is the GCF number.
So the greatest common factor 37314 and 37319 is 1.

Also check out the Least Common Multiple of 37314 and 37319