What is the Greatest Common Factor of 37404 and 37414?

Greatest common factor (GCF) of 37404 and 37414 is 2.

GCF(37404,37414) = 2

We will now calculate the prime factors of 37404 and 37414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37404 and 37414.

How to find the GCF of 37404 and 37414?

We will first find the prime factorization of 37404 and 37414. After we will calculate the factors of 37404 and 37414 and find the biggest common factor number .

Step-1: Prime Factorization of 37404

Prime factors of 37404 are 2, 3, 1039. Prime factorization of 37404 in exponential form is:

37404 = 2² × 3² × 1039¹

Step-2: Prime Factorization of 37414

Prime factors of 37414 are 2, 13, 1439. Prime factorization of 37414 in exponential form is:

37414 = 2¹ × 13¹ × 1439¹

Step-3: Factors of 37404

List of positive integer factors of 37404 that divides 37404 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1039, 2078, 3117, 4156, 6234, 9351, 12468, 18702

Step-4: Factors of 37414

List of positive integer factors of 37414 that divides 37404 without a remainder.

1, 2, 13, 26, 1439, 2878, 18707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37404 and 37414. The biggest common factor number is the GCF number.
So the greatest common factor 37404 and 37414 is 2.

Also check out the Least Common Multiple of 37404 and 37414