What is the Greatest Common Factor of 32800 and 32816?

Greatest common factor (GCF) of 32800 and 32816 is 16.

GCF(32800,32816) = 16

We will now calculate the prime factors of 32800 and 32816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32800 and 32816.

How to find the GCF of 32800 and 32816?

We will first find the prime factorization of 32800 and 32816. After we will calculate the factors of 32800 and 32816 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 32816

Prime factors of 32816 are 2, 7, 293. Prime factorization of 32816 in exponential form is:

32816 = 2⁴ × 7¹ × 293¹

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 32816

List of positive integer factors of 32816 that divides 32800 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 293, 586, 1172, 2051, 2344, 4102, 4688, 8204, 16408

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32800 and 32816. The biggest common factor number is the GCF number.
So the greatest common factor 32800 and 32816 is 16.

Also check out the Least Common Multiple of 32800 and 32816