What is the Greatest Common Factor of 33785 and 33800?

Greatest common factor (GCF) of 33785 and 33800 is 5.

GCF(33785,33800) = 5

We will now calculate the prime factors of 33785 and 33800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33785 and 33800.

How to find the GCF of 33785 and 33800?

We will first find the prime factorization of 33785 and 33800. After we will calculate the factors of 33785 and 33800 and find the biggest common factor number .

Step-1: Prime Factorization of 33785

Prime factors of 33785 are 5, 29, 233. Prime factorization of 33785 in exponential form is:

33785 = 5¹ × 29¹ × 233¹

Step-2: Prime Factorization of 33800

Prime factors of 33800 are 2, 5, 13. Prime factorization of 33800 in exponential form is:

33800 = 2³ × 5² × 13²

Step-3: Factors of 33785

List of positive integer factors of 33785 that divides 33785 without a remainder.

1, 5, 29, 145, 233, 1165, 6757

Step-4: Factors of 33800

List of positive integer factors of 33800 that divides 33785 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 169, 200, 260, 325, 338, 520, 650, 676, 845, 1300, 1352, 1690, 2600, 3380, 4225, 6760, 8450, 16900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33785 and 33800. The biggest common factor number is the GCF number.
So the greatest common factor 33785 and 33800 is 5.

Also check out the Least Common Multiple of 33785 and 33800