What is the Greatest Common Factor of 37590 and 37600?

Greatest common factor (GCF) of 37590 and 37600 is 10.

GCF(37590,37600) = 10

We will now calculate the prime factors of 37590 and 37600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37590 and 37600.

How to find the GCF of 37590 and 37600?

We will first find the prime factorization of 37590 and 37600. After we will calculate the factors of 37590 and 37600 and find the biggest common factor number .

Step-1: Prime Factorization of 37590

Prime factors of 37590 are 2, 3, 5, 7, 179. Prime factorization of 37590 in exponential form is:

37590 = 2¹ × 3¹ × 5¹ × 7¹ × 179¹

Step-2: Prime Factorization of 37600

Prime factors of 37600 are 2, 5, 47. Prime factorization of 37600 in exponential form is:

37600 = 2⁵ × 5² × 47¹

Step-3: Factors of 37590

List of positive integer factors of 37590 that divides 37590 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 179, 210, 358, 537, 895, 1074, 1253, 1790, 2506, 2685, 3759, 5370, 6265, 7518, 12530, 18795

Step-4: Factors of 37600

List of positive integer factors of 37600 that divides 37590 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 47, 50, 80, 94, 100, 160, 188, 200, 235, 376, 400, 470, 752, 800, 940, 1175, 1504, 1880, 2350, 3760, 4700, 7520, 9400, 18800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37590 and 37600. The biggest common factor number is the GCF number.
So the greatest common factor 37590 and 37600 is 10.

Also check out the Least Common Multiple of 37590 and 37600