What is the Greatest Common Factor of 37214 and 37228?

Greatest common factor (GCF) of 37214 and 37228 is 2.

GCF(37214,37228) = 2

We will now calculate the prime factors of 37214 and 37228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37214 and 37228.

How to find the GCF of 37214 and 37228?

We will first find the prime factorization of 37214 and 37228. After we will calculate the factors of 37214 and 37228 and find the biggest common factor number .

Step-1: Prime Factorization of 37214

Prime factors of 37214 are 2, 23, 809. Prime factorization of 37214 in exponential form is:

37214 = 2¹ × 23¹ × 809¹

Step-2: Prime Factorization of 37228

Prime factors of 37228 are 2, 41, 227. Prime factorization of 37228 in exponential form is:

37228 = 2² × 41¹ × 227¹

Step-3: Factors of 37214

List of positive integer factors of 37214 that divides 37214 without a remainder.

1, 2, 23, 46, 809, 1618, 18607

Step-4: Factors of 37228

List of positive integer factors of 37228 that divides 37214 without a remainder.

1, 2, 4, 41, 82, 164, 227, 454, 908, 9307, 18614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37214 and 37228. The biggest common factor number is the GCF number.
So the greatest common factor 37214 and 37228 is 2.

Also check out the Least Common Multiple of 37214 and 37228