What is the Greatest Common Factor of 34785 and 34800?

Greatest common factor (GCF) of 34785 and 34800 is 15.

GCF(34785,34800) = 15

We will now calculate the prime factors of 34785 and 34800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34785 and 34800.

How to find the GCF of 34785 and 34800?

We will first find the prime factorization of 34785 and 34800. After we will calculate the factors of 34785 and 34800 and find the biggest common factor number .

Step-1: Prime Factorization of 34785

Prime factors of 34785 are 3, 5, 773. Prime factorization of 34785 in exponential form is:

34785 = 3² × 5¹ × 773¹

Step-2: Prime Factorization of 34800

Prime factors of 34800 are 2, 3, 5, 29. Prime factorization of 34800 in exponential form is:

34800 = 2⁴ × 3¹ × 5² × 29¹

Step-3: Factors of 34785

List of positive integer factors of 34785 that divides 34785 without a remainder.

1, 3, 5, 9, 15, 45, 773, 2319, 3865, 6957, 11595

Step-4: Factors of 34800

List of positive integer factors of 34800 that divides 34785 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 40, 48, 50, 58, 60, 75, 80, 87, 100, 116, 120, 145, 150, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 580, 600, 696, 725, 870, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2900, 3480, 4350, 5800, 6960, 8700, 11600, 17400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34785 and 34800. The biggest common factor number is the GCF number.
So the greatest common factor 34785 and 34800 is 15.

Also check out the Least Common Multiple of 34785 and 34800