What is the Greatest Common Factor of 37314 and 37320?

Greatest common factor (GCF) of 37314 and 37320 is 6.

GCF(37314,37320) = 6

We will now calculate the prime factors of 37314 and 37320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37314 and 37320.

How to find the GCF of 37314 and 37320?

We will first find the prime factorization of 37314 and 37320. After we will calculate the factors of 37314 and 37320 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 37320

Prime factors of 37320 are 2, 3, 5, 311. Prime factorization of 37320 in exponential form is:

37320 = 2³ × 3¹ × 5¹ × 311¹

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 37320

List of positive integer factors of 37320 that divides 37314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 311, 622, 933, 1244, 1555, 1866, 2488, 3110, 3732, 4665, 6220, 7464, 9330, 12440, 18660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37314 and 37320. The biggest common factor number is the GCF number.
So the greatest common factor 37314 and 37320 is 6.

Also check out the Least Common Multiple of 37314 and 37320