What is the Greatest Common Factor of 37695 and 37700?

Greatest common factor (GCF) of 37695 and 37700 is 5.

GCF(37695,37700) = 5

We will now calculate the prime factors of 37695 and 37700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37695 and 37700.

How to find the GCF of 37695 and 37700?

We will first find the prime factorization of 37695 and 37700. After we will calculate the factors of 37695 and 37700 and find the biggest common factor number .

Step-1: Prime Factorization of 37695

Prime factors of 37695 are 3, 5, 7, 359. Prime factorization of 37695 in exponential form is:

37695 = 3¹ × 5¹ × 7¹ × 359¹

Step-2: Prime Factorization of 37700

Prime factors of 37700 are 2, 5, 13, 29. Prime factorization of 37700 in exponential form is:

37700 = 2² × 5² × 13¹ × 29¹

Step-3: Factors of 37695

List of positive integer factors of 37695 that divides 37695 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 359, 1077, 1795, 2513, 5385, 7539, 12565

Step-4: Factors of 37700

List of positive integer factors of 37700 that divides 37695 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 29, 50, 52, 58, 65, 100, 116, 130, 145, 260, 290, 325, 377, 580, 650, 725, 754, 1300, 1450, 1508, 1885, 2900, 3770, 7540, 9425, 18850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37695 and 37700. The biggest common factor number is the GCF number.
So the greatest common factor 37695 and 37700 is 5.

Also check out the Least Common Multiple of 37695 and 37700