What is the Greatest Common Factor of 37306 and 37314?

Greatest common factor (GCF) of 37306 and 37314 is 2.

GCF(37306,37314) = 2

We will now calculate the prime factors of 37306 and 37314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37306 and 37314.

How to find the GCF of 37306 and 37314?

We will first find the prime factorization of 37306 and 37314. After we will calculate the factors of 37306 and 37314 and find the biggest common factor number .

Step-1: Prime Factorization of 37306

Prime factors of 37306 are 2, 23, 811. Prime factorization of 37306 in exponential form is:

37306 = 2¹ × 23¹ × 811¹

Step-2: 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-3: Factors of 37306

List of positive integer factors of 37306 that divides 37306 without a remainder.

1, 2, 23, 46, 811, 1622, 18653

Step-4: Factors of 37314

List of positive integer factors of 37314 that divides 37306 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37306 and 37314. The biggest common factor number is the GCF number.
So the greatest common factor 37306 and 37314 is 2.

Also check out the Least Common Multiple of 37306 and 37314