What is the Greatest Common Factor of 37724 and 37728?

Greatest common factor (GCF) of 37724 and 37728 is 4.

GCF(37724,37728) = 4

We will now calculate the prime factors of 37724 and 37728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37724 and 37728.

How to find the GCF of 37724 and 37728?

We will first find the prime factorization of 37724 and 37728. After we will calculate the factors of 37724 and 37728 and find the biggest common factor number .

Step-1: Prime Factorization of 37724

Prime factors of 37724 are 2, 9431. Prime factorization of 37724 in exponential form is:

37724 = 2² × 9431¹

Step-2: Prime Factorization of 37728

Prime factors of 37728 are 2, 3, 131. Prime factorization of 37728 in exponential form is:

37728 = 2⁵ × 3² × 131¹

Step-3: Factors of 37724

List of positive integer factors of 37724 that divides 37724 without a remainder.

1, 2, 4, 9431, 18862

Step-4: Factors of 37728

List of positive integer factors of 37728 that divides 37724 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 131, 144, 262, 288, 393, 524, 786, 1048, 1179, 1572, 2096, 2358, 3144, 4192, 4716, 6288, 9432, 12576, 18864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37724 and 37728. The biggest common factor number is the GCF number.
So the greatest common factor 37724 and 37728 is 4.

Also check out the Least Common Multiple of 37724 and 37728