What is the Greatest Common Factor of 36792 and 36800?

Greatest common factor (GCF) of 36792 and 36800 is 8.

GCF(36792,36800) = 8

We will now calculate the prime factors of 36792 and 36800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36792 and 36800.

How to find the GCF of 36792 and 36800?

We will first find the prime factorization of 36792 and 36800. After we will calculate the factors of 36792 and 36800 and find the biggest common factor number .

Step-1: Prime Factorization of 36792

Prime factors of 36792 are 2, 3, 7, 73. Prime factorization of 36792 in exponential form is:

36792 = 2³ × 3² × 7¹ × 73¹

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 36792

List of positive integer factors of 36792 that divides 36792 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 73, 84, 126, 146, 168, 219, 252, 292, 438, 504, 511, 584, 657, 876, 1022, 1314, 1533, 1752, 2044, 2628, 3066, 4088, 4599, 5256, 6132, 9198, 12264, 18396

Step-4: Factors of 36800

List of positive integer factors of 36800 that divides 36792 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 36792 and 36800. The biggest common factor number is the GCF number.
So the greatest common factor 36792 and 36800 is 8.

Also check out the Least Common Multiple of 36792 and 36800