What is the Greatest Common Factor of 37600 and 37620?

Greatest common factor (GCF) of 37600 and 37620 is 20.

GCF(37600,37620) = 20

We will now calculate the prime factors of 37600 and 37620, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37600 and 37620.

How to find the GCF of 37600 and 37620?

We will first find the prime factorization of 37600 and 37620. After we will calculate the factors of 37600 and 37620 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37620

Prime factors of 37620 are 2, 3, 5, 11, 19. Prime factorization of 37620 in exponential form is:

37620 = 2² × 3² × 5¹ × 11¹ × 19¹

Step-3: Factors of 37600

List of positive integer factors of 37600 that divides 37600 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

Step-4: Factors of 37620

List of positive integer factors of 37620 that divides 37600 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 19, 20, 22, 30, 33, 36, 38, 44, 45, 55, 57, 60, 66, 76, 90, 95, 99, 110, 114, 132, 165, 171, 180, 190, 198, 209, 220, 228, 285, 330, 342, 380, 396, 418, 495, 570, 627, 660, 684, 836, 855, 990, 1045, 1140, 1254, 1710, 1881, 1980, 2090, 2508, 3135, 3420, 3762, 4180, 6270, 7524, 9405, 12540, 18810

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37600 and 37620. The biggest common factor number is the GCF number.
So the greatest common factor 37600 and 37620 is 20.

Also check out the Least Common Multiple of 37600 and 37620