What is the Greatest Common Factor of 37749 and 37755?

Greatest common factor (GCF) of 37749 and 37755 is 3.

GCF(37749,37755) = 3

We will now calculate the prime factors of 37749 and 37755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37749 and 37755.

How to find the GCF of 37749 and 37755?

We will first find the prime factorization of 37749 and 37755. After we will calculate the factors of 37749 and 37755 and find the biggest common factor number .

Step-1: Prime Factorization of 37749

Prime factors of 37749 are 3, 12583. Prime factorization of 37749 in exponential form is:

37749 = 3¹ × 12583¹

Step-2: Prime Factorization of 37755

Prime factors of 37755 are 3, 5, 839. Prime factorization of 37755 in exponential form is:

37755 = 3² × 5¹ × 839¹

Step-3: Factors of 37749

List of positive integer factors of 37749 that divides 37749 without a remainder.

1, 3, 12583

Step-4: Factors of 37755

List of positive integer factors of 37755 that divides 37749 without a remainder.

1, 3, 5, 9, 15, 45, 839, 2517, 4195, 7551, 12585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37749 and 37755. The biggest common factor number is the GCF number.
So the greatest common factor 37749 and 37755 is 3.

Also check out the Least Common Multiple of 37749 and 37755