What is the Greatest Common Factor of 37800 and 37808?

Greatest common factor (GCF) of 37800 and 37808 is 8.

GCF(37800,37808) = 8

We will now calculate the prime factors of 37800 and 37808, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37800 and 37808.

How to find the GCF of 37800 and 37808?

We will first find the prime factorization of 37800 and 37808. After we will calculate the factors of 37800 and 37808 and find the biggest common factor number .

Step-1: Prime Factorization of 37800

Prime factors of 37800 are 2, 3, 5, 7. Prime factorization of 37800 in exponential form is:

37800 = 2³ × 3³ × 5² × 7¹

Step-2: Prime Factorization of 37808

Prime factors of 37808 are 2, 17, 139. Prime factorization of 37808 in exponential form is:

37808 = 2⁴ × 17¹ × 139¹

Step-3: Factors of 37800

List of positive integer factors of 37800 that divides 37800 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 27, 28, 30, 35, 36, 40, 42, 45, 50, 54, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 108, 120, 126, 135, 140, 150, 168, 175, 180, 189, 200, 210, 216, 225, 252, 270, 280, 300, 315, 350, 360, 378, 420, 450, 504, 525, 540, 600, 630, 675, 700, 756, 840, 900, 945, 1050, 1080, 1260, 1350, 1400, 1512, 1575, 1800, 1890, 2100, 2520, 2700, 3150, 3780, 4200, 4725, 5400, 6300, 7560, 9450, 12600, 18900

Step-4: Factors of 37808

List of positive integer factors of 37808 that divides 37800 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 139, 272, 278, 556, 1112, 2224, 2363, 4726, 9452, 18904

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37800 and 37808. The biggest common factor number is the GCF number.
So the greatest common factor 37800 and 37808 is 8.

Also check out the Least Common Multiple of 37800 and 37808