What is the Greatest Common Factor of 37296 and 37304?

Greatest common factor (GCF) of 37296 and 37304 is 8.

GCF(37296,37304) = 8

We will now calculate the prime factors of 37296 and 37304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37296 and 37304.

How to find the GCF of 37296 and 37304?

We will first find the prime factorization of 37296 and 37304. After we will calculate the factors of 37296 and 37304 and find the biggest common factor number .

Step-1: Prime Factorization of 37296

Prime factors of 37296 are 2, 3, 7, 37. Prime factorization of 37296 in exponential form is:

37296 = 2⁴ × 3² × 7¹ × 37¹

Step-2: Prime Factorization of 37304

Prime factors of 37304 are 2, 4663. Prime factorization of 37304 in exponential form is:

37304 = 2³ × 4663¹

Step-3: Factors of 37296

List of positive integer factors of 37296 that divides 37296 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 37, 42, 48, 56, 63, 72, 74, 84, 111, 112, 126, 144, 148, 168, 222, 252, 259, 296, 333, 336, 444, 504, 518, 592, 666, 777, 888, 1008, 1036, 1332, 1554, 1776, 2072, 2331, 2664, 3108, 4144, 4662, 5328, 6216, 9324, 12432, 18648

Step-4: Factors of 37304

List of positive integer factors of 37304 that divides 37296 without a remainder.

1, 2, 4, 8, 4663, 9326, 18652

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37296 and 37304. The biggest common factor number is the GCF number.
So the greatest common factor 37296 and 37304 is 8.

Also check out the Least Common Multiple of 37296 and 37304