What is the Greatest Common Factor of 32785 and 32800?

Greatest common factor (GCF) of 32785 and 32800 is 5.

GCF(32785,32800) = 5

We will now calculate the prime factors of 32785 and 32800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32785 and 32800.

How to find the GCF of 32785 and 32800?

We will first find the prime factorization of 32785 and 32800. After we will calculate the factors of 32785 and 32800 and find the biggest common factor number .

Step-1: Prime Factorization of 32785

Prime factors of 32785 are 5, 79, 83. Prime factorization of 32785 in exponential form is:

32785 = 5¹ × 79¹ × 83¹

Step-2: 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-3: Factors of 32785

List of positive integer factors of 32785 that divides 32785 without a remainder.

1, 5, 79, 83, 395, 415, 6557

Step-4: Factors of 32800

List of positive integer factors of 32800 that divides 32785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32785 and 32800. The biggest common factor number is the GCF number.
So the greatest common factor 32785 and 32800 is 5.

Also check out the Least Common Multiple of 32785 and 32800