What is the Greatest Common Factor of 17184 and 17200?

Greatest common factor (GCF) of 17184 and 17200 is 16.

GCF(17184,17200) = 16

We will now calculate the prime factors of 17184 and 17200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17184 and 17200.

How to find the GCF of 17184 and 17200?

We will first find the prime factorization of 17184 and 17200. After we will calculate the factors of 17184 and 17200 and find the biggest common factor number .

Step-1: Prime Factorization of 17184

Prime factors of 17184 are 2, 3, 179. Prime factorization of 17184 in exponential form is:

17184 = 2⁵ × 3¹ × 179¹

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 17184

List of positive integer factors of 17184 that divides 17184 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 179, 358, 537, 716, 1074, 1432, 2148, 2864, 4296, 5728, 8592

Step-4: Factors of 17200

List of positive integer factors of 17200 that divides 17184 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 17184 and 17200. The biggest common factor number is the GCF number.
So the greatest common factor 17184 and 17200 is 16.

Also check out the Least Common Multiple of 17184 and 17200