What is the Greatest Common Factor of 37725 and 37734?

Greatest common factor (GCF) of 37725 and 37734 is 3.

GCF(37725,37734) = 3

We will now calculate the prime factors of 37725 and 37734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37725 and 37734.

How to find the GCF of 37725 and 37734?

We will first find the prime factorization of 37725 and 37734. After we will calculate the factors of 37725 and 37734 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 37734

Prime factors of 37734 are 2, 3, 19, 331. Prime factorization of 37734 in exponential form is:

37734 = 2¹ × 3¹ × 19¹ × 331¹

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 37734

List of positive integer factors of 37734 that divides 37725 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 331, 662, 993, 1986, 6289, 12578, 18867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37725 and 37734. The biggest common factor number is the GCF number.
So the greatest common factor 37725 and 37734 is 3.

Also check out the Least Common Multiple of 37725 and 37734