What is the Greatest Common Factor of 37800 and 37815?

Greatest common factor (GCF) of 37800 and 37815 is 15.

GCF(37800,37815) = 15

We will now calculate the prime factors of 37800 and 37815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37800 and 37815.

How to find the GCF of 37800 and 37815?

We will first find the prime factorization of 37800 and 37815. After we will calculate the factors of 37800 and 37815 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 37815

Prime factors of 37815 are 3, 5, 2521. Prime factorization of 37815 in exponential form is:

37815 = 3¹ × 5¹ × 2521¹

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 37815

List of positive integer factors of 37815 that divides 37800 without a remainder.

1, 3, 5, 15, 2521, 7563, 12605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37800 and 37815. The biggest common factor number is the GCF number.
So the greatest common factor 37800 and 37815 is 15.

Also check out the Least Common Multiple of 37800 and 37815