What is the Greatest Common Factor of 37205 and 37219?

Greatest common factor (GCF) of 37205 and 37219 is 7.

GCF(37205,37219) = 7

We will now calculate the prime factors of 37205 and 37219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37205 and 37219.

How to find the GCF of 37205 and 37219?

We will first find the prime factorization of 37205 and 37219. After we will calculate the factors of 37205 and 37219 and find the biggest common factor number .

Step-1: Prime Factorization of 37205

Prime factors of 37205 are 5, 7, 1063. Prime factorization of 37205 in exponential form is:

37205 = 5¹ × 7¹ × 1063¹

Step-2: Prime Factorization of 37219

Prime factors of 37219 are 7, 13, 409. Prime factorization of 37219 in exponential form is:

37219 = 7¹ × 13¹ × 409¹

Step-3: Factors of 37205

List of positive integer factors of 37205 that divides 37205 without a remainder.

1, 5, 7, 35, 1063, 5315, 7441

Step-4: Factors of 37219

List of positive integer factors of 37219 that divides 37205 without a remainder.

1, 7, 13, 91, 409, 2863, 5317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37205 and 37219. The biggest common factor number is the GCF number.
So the greatest common factor 37205 and 37219 is 7.

Also check out the Least Common Multiple of 37205 and 37219