What is the Greatest Common Factor of 33200 and 33216?

Greatest common factor (GCF) of 33200 and 33216 is 16.

GCF(33200,33216) = 16

We will now calculate the prime factors of 33200 and 33216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33200 and 33216.

How to find the GCF of 33200 and 33216?

We will first find the prime factorization of 33200 and 33216. After we will calculate the factors of 33200 and 33216 and find the biggest common factor number .

Step-1: Prime Factorization of 33200

Prime factors of 33200 are 2, 5, 83. Prime factorization of 33200 in exponential form is:

33200 = 2⁴ × 5² × 83¹

Step-2: Prime Factorization of 33216

Prime factors of 33216 are 2, 3, 173. Prime factorization of 33216 in exponential form is:

33216 = 2⁶ × 3¹ × 173¹

Step-3: Factors of 33200

List of positive integer factors of 33200 that divides 33200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 83, 100, 166, 200, 332, 400, 415, 664, 830, 1328, 1660, 2075, 3320, 4150, 6640, 8300, 16600

Step-4: Factors of 33216

List of positive integer factors of 33216 that divides 33200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 173, 192, 346, 519, 692, 1038, 1384, 2076, 2768, 4152, 5536, 8304, 11072, 16608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33200 and 33216. The biggest common factor number is the GCF number.
So the greatest common factor 33200 and 33216 is 16.

Also check out the Least Common Multiple of 33200 and 33216