What is the Greatest Common Factor of 37744 and 37748?

Greatest common factor (GCF) of 37744 and 37748 is 4.

GCF(37744,37748) = 4

We will now calculate the prime factors of 37744 and 37748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37744 and 37748.

How to find the GCF of 37744 and 37748?

We will first find the prime factorization of 37744 and 37748. After we will calculate the factors of 37744 and 37748 and find the biggest common factor number .

Step-1: Prime Factorization of 37744

Prime factors of 37744 are 2, 7, 337. Prime factorization of 37744 in exponential form is:

37744 = 2⁴ × 7¹ × 337¹

Step-2: Prime Factorization of 37748

Prime factors of 37748 are 2, 9437. Prime factorization of 37748 in exponential form is:

37748 = 2² × 9437¹

Step-3: Factors of 37744

List of positive integer factors of 37744 that divides 37744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 337, 674, 1348, 2359, 2696, 4718, 5392, 9436, 18872

Step-4: Factors of 37748

List of positive integer factors of 37748 that divides 37744 without a remainder.

1, 2, 4, 9437, 18874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37744 and 37748. The biggest common factor number is the GCF number.
So the greatest common factor 37744 and 37748 is 4.

Also check out the Least Common Multiple of 37744 and 37748