What is the Greatest Common Factor of 37725 and 37740?

Greatest common factor (GCF) of 37725 and 37740 is 15.

GCF(37725,37740) = 15

We will now calculate the prime factors of 37725 and 37740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37725 and 37740.

How to find the GCF of 37725 and 37740?

We will first find the prime factorization of 37725 and 37740. After we will calculate the factors of 37725 and 37740 and find the biggest common factor number .

Step-1: Prime Factorization of 37725

Prime factors of 37725 are 3, 5, 503. Prime factorization of 37725 in exponential form is:

37725 = 3¹ × 5² × 503¹

Step-2: Prime Factorization of 37740

Prime factors of 37740 are 2, 3, 5, 17, 37. Prime factorization of 37740 in exponential form is:

37740 = 2² × 3¹ × 5¹ × 17¹ × 37¹

Step-3: Factors of 37725

List of positive integer factors of 37725 that divides 37725 without a remainder.

1, 3, 5, 15, 25, 75, 503, 1509, 2515, 7545, 12575

Step-4: Factors of 37740

List of positive integer factors of 37740 that divides 37725 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 37, 51, 60, 68, 74, 85, 102, 111, 148, 170, 185, 204, 222, 255, 340, 370, 444, 510, 555, 629, 740, 1020, 1110, 1258, 1887, 2220, 2516, 3145, 3774, 6290, 7548, 9435, 12580, 18870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37725 and 37740. The biggest common factor number is the GCF number.
So the greatest common factor 37725 and 37740 is 15.

Also check out the Least Common Multiple of 37725 and 37740