What is the Greatest Common Factor of 37680 and 37700?

Greatest common factor (GCF) of 37680 and 37700 is 20.

GCF(37680,37700) = 20

We will now calculate the prime factors of 37680 and 37700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37680 and 37700.

How to find the GCF of 37680 and 37700?

We will first find the prime factorization of 37680 and 37700. After we will calculate the factors of 37680 and 37700 and find the biggest common factor number .

Step-1: Prime Factorization of 37680

Prime factors of 37680 are 2, 3, 5, 157. Prime factorization of 37680 in exponential form is:

37680 = 2⁴ × 3¹ × 5¹ × 157¹

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 37680

List of positive integer factors of 37680 that divides 37680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840

Step-4: Factors of 37700

List of positive integer factors of 37700 that divides 37680 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 37680 and 37700. The biggest common factor number is the GCF number.
So the greatest common factor 37680 and 37700 is 20.

Also check out the Least Common Multiple of 37680 and 37700