What is the Greatest Common Factor of 17289 and 17304?

Greatest common factor (GCF) of 17289 and 17304 is 3.

GCF(17289,17304) = 3

We will now calculate the prime factors of 17289 and 17304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17289 and 17304.

How to find the GCF of 17289 and 17304?

We will first find the prime factorization of 17289 and 17304. After we will calculate the factors of 17289 and 17304 and find the biggest common factor number .

Step-1: Prime Factorization of 17289

Prime factors of 17289 are 3, 17, 113. Prime factorization of 17289 in exponential form is:

17289 = 3² × 17¹ × 113¹

Step-2: Prime Factorization of 17304

Prime factors of 17304 are 2, 3, 7, 103. Prime factorization of 17304 in exponential form is:

17304 = 2³ × 3¹ × 7¹ × 103¹

Step-3: Factors of 17289

List of positive integer factors of 17289 that divides 17289 without a remainder.

1, 3, 9, 17, 51, 113, 153, 339, 1017, 1921, 5763

Step-4: Factors of 17304

List of positive integer factors of 17304 that divides 17289 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 103, 168, 206, 309, 412, 618, 721, 824, 1236, 1442, 2163, 2472, 2884, 4326, 5768, 8652

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17289 and 17304. The biggest common factor number is the GCF number.
So the greatest common factor 17289 and 17304 is 3.

Also check out the Least Common Multiple of 17289 and 17304