What is the Greatest Common Factor of 37538 and 37548?

Greatest common factor (GCF) of 37538 and 37548 is 2.

GCF(37538,37548) = 2

We will now calculate the prime factors of 37538 and 37548, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37538 and 37548.

How to find the GCF of 37538 and 37548?

We will first find the prime factorization of 37538 and 37548. After we will calculate the factors of 37538 and 37548 and find the biggest common factor number .

Step-1: Prime Factorization of 37538

Prime factors of 37538 are 2, 137. Prime factorization of 37538 in exponential form is:

37538 = 2¹ × 137²

Step-2: Prime Factorization of 37548

Prime factors of 37548 are 2, 3, 7, 149. Prime factorization of 37548 in exponential form is:

37548 = 2² × 3² × 7¹ × 149¹

Step-3: Factors of 37538

List of positive integer factors of 37538 that divides 37538 without a remainder.

1, 2, 137, 274, 18769

Step-4: Factors of 37548

List of positive integer factors of 37548 that divides 37538 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 149, 252, 298, 447, 596, 894, 1043, 1341, 1788, 2086, 2682, 3129, 4172, 5364, 6258, 9387, 12516, 18774

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37538 and 37548. The biggest common factor number is the GCF number.
So the greatest common factor 37538 and 37548 is 2.

Also check out the Least Common Multiple of 37538 and 37548