What is the Greatest Common Factor of 37635 and 37648?

Greatest common factor (GCF) of 37635 and 37648 is 13.

GCF(37635,37648) = 13

We will now calculate the prime factors of 37635 and 37648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37635 and 37648.

How to find the GCF of 37635 and 37648?

We will first find the prime factorization of 37635 and 37648. After we will calculate the factors of 37635 and 37648 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37648

Prime factors of 37648 are 2, 13, 181. Prime factorization of 37648 in exponential form is:

37648 = 2⁴ × 13¹ × 181¹

Step-3: Factors of 37635

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

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

Step-4: Factors of 37648

List of positive integer factors of 37648 that divides 37635 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 181, 208, 362, 724, 1448, 2353, 2896, 4706, 9412, 18824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37635 and 37648. The biggest common factor number is the GCF number.
So the greatest common factor 37635 and 37648 is 13.

Also check out the Least Common Multiple of 37635 and 37648