What is the Greatest Common Factor of 17184 and 17199?

Greatest common factor (GCF) of 17184 and 17199 is 3.

GCF(17184,17199) = 3

We will now calculate the prime factors of 17184 and 17199, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17184 and 17199.

How to find the GCF of 17184 and 17199?

We will first find the prime factorization of 17184 and 17199. After we will calculate the factors of 17184 and 17199 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 17199

Prime factors of 17199 are 3, 7, 13. Prime factorization of 17199 in exponential form is:

17199 = 3³ × 7² × 13¹

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 17199

List of positive integer factors of 17199 that divides 17184 without a remainder.

1, 3, 7, 9, 13, 21, 27, 39, 49, 63, 91, 117, 147, 189, 273, 351, 441, 637, 819, 1323, 1911, 2457, 5733

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17184 and 17199. The biggest common factor number is the GCF number.
So the greatest common factor 17184 and 17199 is 3.

Also check out the Least Common Multiple of 17184 and 17199