What is the Greatest Common Factor of 3200 and 3210?

Greatest common factor (GCF) of 3200 and 3210 is 10.

GCF(3200,3210) = 10

We will now calculate the prime factors of 3200 and 3210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3200 and 3210.

How to find the GCF of 3200 and 3210?

We will first find the prime factorization of 3200 and 3210. After we will calculate the factors of 3200 and 3210 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 3210

Prime factors of 3210 are 2, 3, 5, 107. Prime factorization of 3210 in exponential form is:

3210 = 2¹ × 3¹ × 5¹ × 107¹

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 3210

List of positive integer factors of 3210 that divides 3200 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 107, 214, 321, 535, 642, 1070, 1605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3200 and 3210. The biggest common factor number is the GCF number.
So the greatest common factor 3200 and 3210 is 10.

Also check out the Least Common Multiple of 3200 and 3210