What is the Greatest Common Factor of 36784 and 36800?

Greatest common factor (GCF) of 36784 and 36800 is 16.

GCF(36784,36800) = 16

We will now calculate the prime factors of 36784 and 36800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36784 and 36800.

How to find the GCF of 36784 and 36800?

We will first find the prime factorization of 36784 and 36800. After we will calculate the factors of 36784 and 36800 and find the biggest common factor number .

Step-1: Prime Factorization of 36784

Prime factors of 36784 are 2, 11, 19. Prime factorization of 36784 in exponential form is:

36784 = 2⁴ × 11² × 19¹

Step-2: 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-3: Factors of 36784

List of positive integer factors of 36784 that divides 36784 without a remainder.

1, 2, 4, 8, 11, 16, 19, 22, 38, 44, 76, 88, 121, 152, 176, 209, 242, 304, 418, 484, 836, 968, 1672, 1936, 2299, 3344, 4598, 9196, 18392

Step-4: Factors of 36800

List of positive integer factors of 36800 that divides 36784 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36784 and 36800. The biggest common factor number is the GCF number.
So the greatest common factor 36784 and 36800 is 16.

Also check out the Least Common Multiple of 36784 and 36800