What is the Greatest Common Factor of 34800 and 34815?

Greatest common factor (GCF) of 34800 and 34815 is 15.

GCF(34800,34815) = 15

We will now calculate the prime factors of 34800 and 34815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34800 and 34815.

How to find the GCF of 34800 and 34815?

We will first find the prime factorization of 34800 and 34815. After we will calculate the factors of 34800 and 34815 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34815

Prime factors of 34815 are 3, 5, 11, 211. Prime factorization of 34815 in exponential form is:

34815 = 3¹ × 5¹ × 11¹ × 211¹

Step-3: Factors of 34800

List of positive integer factors of 34800 that divides 34800 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

Step-4: Factors of 34815

List of positive integer factors of 34815 that divides 34800 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 211, 633, 1055, 2321, 3165, 6963, 11605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34800 and 34815. The biggest common factor number is the GCF number.
So the greatest common factor 34800 and 34815 is 15.

Also check out the Least Common Multiple of 34800 and 34815