What is the Greatest Common Factor of 32800 and 32810?

Greatest common factor (GCF) of 32800 and 32810 is 10.

GCF(32800,32810) = 10

We will now calculate the prime factors of 32800 and 32810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32800 and 32810.

How to find the GCF of 32800 and 32810?

We will first find the prime factorization of 32800 and 32810. After we will calculate the factors of 32800 and 32810 and find the biggest common factor number .

Step-1: Prime Factorization of 32800

Prime factors of 32800 are 2, 5, 41. Prime factorization of 32800 in exponential form is:

32800 = 2⁵ × 5² × 41¹

Step-2: Prime Factorization of 32810

Prime factors of 32810 are 2, 5, 17, 193. Prime factorization of 32810 in exponential form is:

32810 = 2¹ × 5¹ × 17¹ × 193¹

Step-3: Factors of 32800

List of positive integer factors of 32800 that divides 32800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 41, 50, 80, 82, 100, 160, 164, 200, 205, 328, 400, 410, 656, 800, 820, 1025, 1312, 1640, 2050, 3280, 4100, 6560, 8200, 16400

Step-4: Factors of 32810

List of positive integer factors of 32810 that divides 32800 without a remainder.

1, 2, 5, 10, 17, 34, 85, 170, 193, 386, 965, 1930, 3281, 6562, 16405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32800 and 32810. The biggest common factor number is the GCF number.
So the greatest common factor 32800 and 32810 is 10.

Also check out the Least Common Multiple of 32800 and 32810