What is the Greatest Common Factor of 37282 and 37296?

Greatest common factor (GCF) of 37282 and 37296 is 14.

GCF(37282,37296) = 14

We will now calculate the prime factors of 37282 and 37296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37282 and 37296.

How to find the GCF of 37282 and 37296?

We will first find the prime factorization of 37282 and 37296. After we will calculate the factors of 37282 and 37296 and find the biggest common factor number .

Step-1: Prime Factorization of 37282

Prime factors of 37282 are 2, 7, 2663. Prime factorization of 37282 in exponential form is:

37282 = 2¹ × 7¹ × 2663¹

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 37282

List of positive integer factors of 37282 that divides 37282 without a remainder.

1, 2, 7, 14, 2663, 5326, 18641

Step-4: Factors of 37296

List of positive integer factors of 37296 that divides 37282 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 37282 and 37296. The biggest common factor number is the GCF number.
So the greatest common factor 37282 and 37296 is 14.

Also check out the Least Common Multiple of 37282 and 37296