What is the Greatest Common Factor of 37140 and 37149?

Greatest common factor (GCF) of 37140 and 37149 is 3.

GCF(37140,37149) = 3

We will now calculate the prime factors of 37140 and 37149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37140 and 37149.

How to find the GCF of 37140 and 37149?

We will first find the prime factorization of 37140 and 37149. After we will calculate the factors of 37140 and 37149 and find the biggest common factor number .

Step-1: Prime Factorization of 37140

Prime factors of 37140 are 2, 3, 5, 619. Prime factorization of 37140 in exponential form is:

37140 = 2² × 3¹ × 5¹ × 619¹

Step-2: Prime Factorization of 37149

Prime factors of 37149 are 3, 7, 29, 61. Prime factorization of 37149 in exponential form is:

37149 = 3¹ × 7¹ × 29¹ × 61¹

Step-3: Factors of 37140

List of positive integer factors of 37140 that divides 37140 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 619, 1238, 1857, 2476, 3095, 3714, 6190, 7428, 9285, 12380, 18570

Step-4: Factors of 37149

List of positive integer factors of 37149 that divides 37140 without a remainder.

1, 3, 7, 21, 29, 61, 87, 183, 203, 427, 609, 1281, 1769, 5307, 12383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37140 and 37149. The biggest common factor number is the GCF number.
So the greatest common factor 37140 and 37149 is 3.

Also check out the Least Common Multiple of 37140 and 37149