What is the Greatest Common Factor of 17200 and 17216?

Greatest common factor (GCF) of 17200 and 17216 is 16.

GCF(17200,17216) = 16

We will now calculate the prime factors of 17200 and 17216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17200 and 17216.

How to find the GCF of 17200 and 17216?

We will first find the prime factorization of 17200 and 17216. After we will calculate the factors of 17200 and 17216 and find the biggest common factor number .

Step-1: Prime Factorization of 17200

Prime factors of 17200 are 2, 5, 43. Prime factorization of 17200 in exponential form is:

17200 = 2⁴ × 5² × 43¹

Step-2: Prime Factorization of 17216

Prime factors of 17216 are 2, 269. Prime factorization of 17216 in exponential form is:

17216 = 2⁶ × 269¹

Step-3: Factors of 17200

List of positive integer factors of 17200 that divides 17200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 43, 50, 80, 86, 100, 172, 200, 215, 344, 400, 430, 688, 860, 1075, 1720, 2150, 3440, 4300, 8600

Step-4: Factors of 17216

List of positive integer factors of 17216 that divides 17200 without a remainder.

1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17200 and 17216. The biggest common factor number is the GCF number.
So the greatest common factor 17200 and 17216 is 16.

Also check out the Least Common Multiple of 17200 and 17216