What is the Greatest Common Factor of 3200 and 3216?

Greatest common factor (GCF) of 3200 and 3216 is 16.

GCF(3200,3216) = 16

We will now calculate the prime factors of 3200 and 3216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3200 and 3216.

How to find the GCF of 3200 and 3216?

We will first find the prime factorization of 3200 and 3216. After we will calculate the factors of 3200 and 3216 and find the biggest common factor number .

Step-1: Prime Factorization of 3200

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

3200 = 2⁷ × 5²

Step-2: Prime Factorization of 3216

Prime factors of 3216 are 2, 3, 67. Prime factorization of 3216 in exponential form is:

3216 = 2⁴ × 3¹ × 67¹

Step-3: Factors of 3200

List of positive integer factors of 3200 that divides 3200 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

Step-4: Factors of 3216

List of positive integer factors of 3216 that divides 3200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 67, 134, 201, 268, 402, 536, 804, 1072, 1608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3200 and 3216. The biggest common factor number is the GCF number.
So the greatest common factor 3200 and 3216 is 16.

Also check out the Least Common Multiple of 3200 and 3216