What is the Greatest Common Factor of 17186 and 17200?

Greatest common factor (GCF) of 17186 and 17200 is 2.

GCF(17186,17200) = 2

We will now calculate the prime factors of 17186 and 17200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17186 and 17200.

How to find the GCF of 17186 and 17200?

We will first find the prime factorization of 17186 and 17200. After we will calculate the factors of 17186 and 17200 and find the biggest common factor number .

Step-1: Prime Factorization of 17186

Prime factors of 17186 are 2, 13, 661. Prime factorization of 17186 in exponential form is:

17186 = 2¹ × 13¹ × 661¹

Step-2: 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-3: Factors of 17186

List of positive integer factors of 17186 that divides 17186 without a remainder.

1, 2, 13, 26, 661, 1322, 8593

Step-4: Factors of 17200

List of positive integer factors of 17200 that divides 17186 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17186 and 17200. The biggest common factor number is the GCF number.
So the greatest common factor 17186 and 17200 is 2.

Also check out the Least Common Multiple of 17186 and 17200