What is the Greatest Common Factor of 37734 and 37749?

Greatest common factor (GCF) of 37734 and 37749 is 3.

GCF(37734,37749) = 3

We will now calculate the prime factors of 37734 and 37749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37734 and 37749.

How to find the GCF of 37734 and 37749?

We will first find the prime factorization of 37734 and 37749. After we will calculate the factors of 37734 and 37749 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37749

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

37749 = 3¹ × 12583¹

Step-3: Factors of 37734

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

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

Step-4: Factors of 37749

List of positive integer factors of 37749 that divides 37734 without a remainder.

1, 3, 12583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37734 and 37749. The biggest common factor number is the GCF number.
So the greatest common factor 37734 and 37749 is 3.

Also check out the Least Common Multiple of 37734 and 37749