What is the Greatest Common Factor of 37909 and 37920?

Greatest common factor (GCF) of 37909 and 37920 is 1.

GCF(37909,37920) = 1

We will now calculate the prime factors of 37909 and 37920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37909 and 37920.

How to find the GCF of 37909 and 37920?

We will first find the prime factorization of 37909 and 37920. After we will calculate the factors of 37909 and 37920 and find the biggest common factor number .

Step-1: Prime Factorization of 37909

Prime factors of 37909 are 167, 227. Prime factorization of 37909 in exponential form is:

37909 = 167¹ × 227¹

Step-2: Prime Factorization of 37920

Prime factors of 37920 are 2, 3, 5, 79. Prime factorization of 37920 in exponential form is:

37920 = 2⁵ × 3¹ × 5¹ × 79¹

Step-3: Factors of 37909

List of positive integer factors of 37909 that divides 37909 without a remainder.

1, 167, 227

Step-4: Factors of 37920

List of positive integer factors of 37920 that divides 37909 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 79, 80, 96, 120, 158, 160, 237, 240, 316, 395, 474, 480, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 6320, 7584, 9480, 12640, 18960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37909 and 37920. The biggest common factor number is the GCF number.
So the greatest common factor 37909 and 37920 is 1.

Also check out the Least Common Multiple of 37909 and 37920