What is the Greatest Common Factor of 3184 and 3200?

Greatest common factor (GCF) of 3184 and 3200 is 16.

GCF(3184,3200) = 16

We will now calculate the prime factors of 3184 and 3200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3184 and 3200.

How to find the GCF of 3184 and 3200?

We will first find the prime factorization of 3184 and 3200. After we will calculate the factors of 3184 and 3200 and find the biggest common factor number .

Step-1: Prime Factorization of 3184

Prime factors of 3184 are 2, 199. Prime factorization of 3184 in exponential form is:

3184 = 2⁴ × 199¹

Step-2: Prime Factorization of 3200

Prime factors of 3200 are 2, 5. Prime factorization of 3200 in exponential form is:

3200 = 2⁷ × 5²

Step-3: Factors of 3184

List of positive integer factors of 3184 that divides 3184 without a remainder.

1, 2, 4, 8, 16, 199, 398, 796, 1592

Step-4: Factors of 3200

List of positive integer factors of 3200 that divides 3184 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3184 and 3200. The biggest common factor number is the GCF number.
So the greatest common factor 3184 and 3200 is 16.

Also check out the Least Common Multiple of 3184 and 3200