What is the Greatest Common Factor of 37289 and 37296?

Greatest common factor (GCF) of 37289 and 37296 is 7.

GCF(37289,37296) = 7

We will now calculate the prime factors of 37289 and 37296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37289 and 37296.

How to find the GCF of 37289 and 37296?

We will first find the prime factorization of 37289 and 37296. After we will calculate the factors of 37289 and 37296 and find the biggest common factor number .

Step-1: Prime Factorization of 37289

Prime factors of 37289 are 7, 761. Prime factorization of 37289 in exponential form is:

37289 = 7² × 761¹

Step-2: 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-3: Factors of 37289

List of positive integer factors of 37289 that divides 37289 without a remainder.

1, 7, 49, 761, 5327

Step-4: Factors of 37296

List of positive integer factors of 37296 that divides 37289 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37289 and 37296. The biggest common factor number is the GCF number.
So the greatest common factor 37289 and 37296 is 7.

Also check out the Least Common Multiple of 37289 and 37296