What is the Greatest Common Factor of 3200 and 3213?

Greatest common factor (GCF) of 3200 and 3213 is 1.

GCF(3200,3213) = 1

We will now calculate the prime factors of 3200 and 3213, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3200 and 3213.

How to find the GCF of 3200 and 3213?

We will first find the prime factorization of 3200 and 3213. After we will calculate the factors of 3200 and 3213 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 3213

Prime factors of 3213 are 3, 7, 17. Prime factorization of 3213 in exponential form is:

3213 = 3³ × 7¹ × 17¹

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 3213

List of positive integer factors of 3213 that divides 3200 without a remainder.

1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3200 and 3213. The biggest common factor number is the GCF number.
So the greatest common factor 3200 and 3213 is 1.

Also check out the Least Common Multiple of 3200 and 3213