What is the Greatest Common Factor of 37125 and 37138?

Greatest common factor (GCF) of 37125 and 37138 is 1.

GCF(37125,37138) = 1

We will now calculate the prime factors of 37125 and 37138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37125 and 37138.

How to find the GCF of 37125 and 37138?

We will first find the prime factorization of 37125 and 37138. After we will calculate the factors of 37125 and 37138 and find the biggest common factor number .

Step-1: Prime Factorization of 37125

Prime factors of 37125 are 3, 5, 11. Prime factorization of 37125 in exponential form is:

37125 = 3³ × 5³ × 11¹

Step-2: Prime Factorization of 37138

Prime factors of 37138 are 2, 31, 599. Prime factorization of 37138 in exponential form is:

37138 = 2¹ × 31¹ × 599¹

Step-3: Factors of 37125

List of positive integer factors of 37125 that divides 37125 without a remainder.

1, 3, 5, 9, 11, 15, 25, 27, 33, 45, 55, 75, 99, 125, 135, 165, 225, 275, 297, 375, 495, 675, 825, 1125, 1375, 1485, 2475, 3375, 4125, 7425, 12375

Step-4: Factors of 37138

List of positive integer factors of 37138 that divides 37125 without a remainder.

1, 2, 31, 62, 599, 1198, 18569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37125 and 37138. The biggest common factor number is the GCF number.
So the greatest common factor 37125 and 37138 is 1.

Also check out the Least Common Multiple of 37125 and 37138