What is the Greatest Common Factor of 37789 and 37800?

Greatest common factor (GCF) of 37789 and 37800 is 1.

GCF(37789,37800) = 1

We will now calculate the prime factors of 37789 and 37800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37789 and 37800.

How to find the GCF of 37789 and 37800?

We will first find the prime factorization of 37789 and 37800. After we will calculate the factors of 37789 and 37800 and find the biggest common factor number .

Step-1: Prime Factorization of 37789

Prime factors of 37789 are 23, 31, 53. Prime factorization of 37789 in exponential form is:

37789 = 23¹ × 31¹ × 53¹

Step-2: 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-3: Factors of 37789

List of positive integer factors of 37789 that divides 37789 without a remainder.

1, 23, 31, 53, 713, 1219, 1643

Step-4: Factors of 37800

List of positive integer factors of 37800 that divides 37789 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37789 and 37800. The biggest common factor number is the GCF number.
So the greatest common factor 37789 and 37800 is 1.

Also check out the Least Common Multiple of 37789 and 37800