What is the Greatest Common Factor of 17290 and 17304?

Greatest common factor (GCF) of 17290 and 17304 is 14.

GCF(17290,17304) = 14

We will now calculate the prime factors of 17290 and 17304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17290 and 17304.

How to find the GCF of 17290 and 17304?

We will first find the prime factorization of 17290 and 17304. After we will calculate the factors of 17290 and 17304 and find the biggest common factor number .

Step-1: Prime Factorization of 17290

Prime factors of 17290 are 2, 5, 7, 13, 19. Prime factorization of 17290 in exponential form is:

17290 = 2¹ × 5¹ × 7¹ × 13¹ × 19¹

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 17290

List of positive integer factors of 17290 that divides 17290 without a remainder.

1, 2, 5, 7, 10, 13, 14, 19, 26, 35, 38, 65, 70, 91, 95, 130, 133, 182, 190, 247, 266, 455, 494, 665, 910, 1235, 1330, 1729, 2470, 3458, 8645

Step-4: Factors of 17304

List of positive integer factors of 17304 that divides 17290 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 17290 and 17304. The biggest common factor number is the GCF number.
So the greatest common factor 17290 and 17304 is 14.

Also check out the Least Common Multiple of 17290 and 17304