What is the Greatest Common Factor of 37786 and 37800?

Greatest common factor (GCF) of 37786 and 37800 is 14.

GCF(37786,37800) = 14

We will now calculate the prime factors of 37786 and 37800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37786 and 37800.

How to find the GCF of 37786 and 37800?

We will first find the prime factorization of 37786 and 37800. After we will calculate the factors of 37786 and 37800 and find the biggest common factor number .

Step-1: Prime Factorization of 37786

Prime factors of 37786 are 2, 7, 2699. Prime factorization of 37786 in exponential form is:

37786 = 2¹ × 7¹ × 2699¹

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 37786

List of positive integer factors of 37786 that divides 37786 without a remainder.

1, 2, 7, 14, 2699, 5398, 18893

Step-4: Factors of 37800

List of positive integer factors of 37800 that divides 37786 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 37786 and 37800. The biggest common factor number is the GCF number.
So the greatest common factor 37786 and 37800 is 14.

Also check out the Least Common Multiple of 37786 and 37800