What is the Greatest Common Factor of 37629 and 37635?

Greatest common factor (GCF) of 37629 and 37635 is 3.

GCF(37629,37635) = 3

We will now calculate the prime factors of 37629 and 37635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37629 and 37635.

How to find the GCF of 37629 and 37635?

We will first find the prime factorization of 37629 and 37635. After we will calculate the factors of 37629 and 37635 and find the biggest common factor number .

Step-1: Prime Factorization of 37629

Prime factors of 37629 are 3, 37, 113. Prime factorization of 37629 in exponential form is:

37629 = 3² × 37¹ × 113¹

Step-2: Prime Factorization of 37635

Prime factors of 37635 are 3, 5, 13, 193. Prime factorization of 37635 in exponential form is:

37635 = 3¹ × 5¹ × 13¹ × 193¹

Step-3: Factors of 37629

List of positive integer factors of 37629 that divides 37629 without a remainder.

1, 3, 9, 37, 111, 113, 333, 339, 1017, 4181, 12543

Step-4: Factors of 37635

List of positive integer factors of 37635 that divides 37629 without a remainder.

1, 3, 5, 13, 15, 39, 65, 193, 195, 579, 965, 2509, 2895, 7527, 12545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37629 and 37635. The biggest common factor number is the GCF number.
So the greatest common factor 37629 and 37635 is 3.

Also check out the Least Common Multiple of 37629 and 37635