What is the Greatest Common Factor of 17199 and 17205?

Greatest common factor (GCF) of 17199 and 17205 is 3.

GCF(17199,17205) = 3

We will now calculate the prime factors of 17199 and 17205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17199 and 17205.

How to find the GCF of 17199 and 17205?

We will first find the prime factorization of 17199 and 17205. After we will calculate the factors of 17199 and 17205 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17205

Prime factors of 17205 are 3, 5, 31, 37. Prime factorization of 17205 in exponential form is:

17205 = 3¹ × 5¹ × 31¹ × 37¹

Step-3: Factors of 17199

List of positive integer factors of 17199 that divides 17199 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

Step-4: Factors of 17205

List of positive integer factors of 17205 that divides 17199 without a remainder.

1, 3, 5, 15, 31, 37, 93, 111, 155, 185, 465, 555, 1147, 3441, 5735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17199 and 17205. The biggest common factor number is the GCF number.
So the greatest common factor 17199 and 17205 is 3.

Also check out the Least Common Multiple of 17199 and 17205