What is the Greatest Common Factor of 36800 and 36810?

Greatest common factor (GCF) of 36800 and 36810 is 10.

GCF(36800,36810) = 10

We will now calculate the prime factors of 36800 and 36810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36800 and 36810.

How to find the GCF of 36800 and 36810?

We will first find the prime factorization of 36800 and 36810. After we will calculate the factors of 36800 and 36810 and find the biggest common factor number .

Step-1: Prime Factorization of 36800

Prime factors of 36800 are 2, 5, 23. Prime factorization of 36800 in exponential form is:

36800 = 2⁶ × 5² × 23¹

Step-2: Prime Factorization of 36810

Prime factors of 36810 are 2, 3, 5, 409. Prime factorization of 36810 in exponential form is:

36810 = 2¹ × 3² × 5¹ × 409¹

Step-3: Factors of 36800

List of positive integer factors of 36800 that divides 36800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80, 92, 100, 115, 160, 184, 200, 230, 320, 368, 400, 460, 575, 736, 800, 920, 1150, 1472, 1600, 1840, 2300, 3680, 4600, 7360, 9200, 18400

Step-4: Factors of 36810

List of positive integer factors of 36810 that divides 36800 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 409, 818, 1227, 2045, 2454, 3681, 4090, 6135, 7362, 12270, 18405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36800 and 36810. The biggest common factor number is the GCF number.
So the greatest common factor 36800 and 36810 is 10.

Also check out the Least Common Multiple of 36800 and 36810