What is the Greatest Common Factor of 37708 and 37728?

Greatest common factor (GCF) of 37708 and 37728 is 4.

GCF(37708,37728) = 4

We will now calculate the prime factors of 37708 and 37728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37708 and 37728.

How to find the GCF of 37708 and 37728?

We will first find the prime factorization of 37708 and 37728. After we will calculate the factors of 37708 and 37728 and find the biggest common factor number .

Step-1: Prime Factorization of 37708

Prime factors of 37708 are 2, 11, 857. Prime factorization of 37708 in exponential form is:

37708 = 2² × 11¹ × 857¹

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 37708

List of positive integer factors of 37708 that divides 37708 without a remainder.

1, 2, 4, 11, 22, 44, 857, 1714, 3428, 9427, 18854

Step-4: Factors of 37728

List of positive integer factors of 37728 that divides 37708 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 37708 and 37728. The biggest common factor number is the GCF number.
So the greatest common factor 37708 and 37728 is 4.

Also check out the Least Common Multiple of 37708 and 37728