What is the Greatest Common Factor of 37205 and 37212?

Greatest common factor (GCF) of 37205 and 37212 is 7.

GCF(37205,37212) = 7

We will now calculate the prime factors of 37205 and 37212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37205 and 37212.

How to find the GCF of 37205 and 37212?

We will first find the prime factorization of 37205 and 37212. After we will calculate the factors of 37205 and 37212 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 37212

Prime factors of 37212 are 2, 3, 7, 443. Prime factorization of 37212 in exponential form is:

37212 = 2² × 3¹ × 7¹ × 443¹

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 37212

List of positive integer factors of 37212 that divides 37205 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 443, 886, 1329, 1772, 2658, 3101, 5316, 6202, 9303, 12404, 18606

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37205 and 37212. The biggest common factor number is the GCF number.
So the greatest common factor 37205 and 37212 is 7.

Also check out the Least Common Multiple of 37205 and 37212