What is the Greatest Common Factor of 37575 and 37590?

Greatest common factor (GCF) of 37575 and 37590 is 15.

GCF(37575,37590) = 15

We will now calculate the prime factors of 37575 and 37590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37575 and 37590.

How to find the GCF of 37575 and 37590?

We will first find the prime factorization of 37575 and 37590. After we will calculate the factors of 37575 and 37590 and find the biggest common factor number .

Step-1: Prime Factorization of 37575

Prime factors of 37575 are 3, 5, 167. Prime factorization of 37575 in exponential form is:

37575 = 3² × 5² × 167¹

Step-2: Prime Factorization of 37590

Prime factors of 37590 are 2, 3, 5, 7, 179. Prime factorization of 37590 in exponential form is:

37590 = 2¹ × 3¹ × 5¹ × 7¹ × 179¹

Step-3: Factors of 37575

List of positive integer factors of 37575 that divides 37575 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 167, 225, 501, 835, 1503, 2505, 4175, 7515, 12525

Step-4: Factors of 37590

List of positive integer factors of 37590 that divides 37575 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 179, 210, 358, 537, 895, 1074, 1253, 1790, 2506, 2685, 3759, 5370, 6265, 7518, 12530, 18795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37575 and 37590. The biggest common factor number is the GCF number.
So the greatest common factor 37575 and 37590 is 15.

Also check out the Least Common Multiple of 37575 and 37590