What is the Greatest Common Factor of 37296 and 37306?

Greatest common factor (GCF) of 37296 and 37306 is 2.

GCF(37296,37306) = 2

We will now calculate the prime factors of 37296 and 37306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37296 and 37306.

How to find the GCF of 37296 and 37306?

We will first find the prime factorization of 37296 and 37306. After we will calculate the factors of 37296 and 37306 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 37306

Prime factors of 37306 are 2, 23, 811. Prime factorization of 37306 in exponential form is:

37306 = 2¹ × 23¹ × 811¹

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 37306

List of positive integer factors of 37306 that divides 37296 without a remainder.

1, 2, 23, 46, 811, 1622, 18653

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37296 and 37306. The biggest common factor number is the GCF number.
So the greatest common factor 37296 and 37306 is 2.

Also check out the Least Common Multiple of 37296 and 37306