What is the Greatest Common Factor of 37205 and 37209?

Greatest common factor (GCF) of 37205 and 37209 is 1.

GCF(37205,37209) = 1

We will now calculate the prime factors of 37205 and 37209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37205 and 37209.

How to find the GCF of 37205 and 37209?

We will first find the prime factorization of 37205 and 37209. After we will calculate the factors of 37205 and 37209 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 37209

Prime factors of 37209 are 3, 79, 157. Prime factorization of 37209 in exponential form is:

37209 = 3¹ × 79¹ × 157¹

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 37209

List of positive integer factors of 37209 that divides 37205 without a remainder.

1, 3, 79, 157, 237, 471, 12403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37205 and 37209. The biggest common factor number is the GCF number.
So the greatest common factor 37205 and 37209 is 1.

Also check out the Least Common Multiple of 37205 and 37209