What is the Greatest Common Factor of 17346 and 17360?

Greatest common factor (GCF) of 17346 and 17360 is 14.

GCF(17346,17360) = 14

We will now calculate the prime factors of 17346 and 17360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17346 and 17360.

How to find the GCF of 17346 and 17360?

We will first find the prime factorization of 17346 and 17360. After we will calculate the factors of 17346 and 17360 and find the biggest common factor number .

Step-1: Prime Factorization of 17346

Prime factors of 17346 are 2, 3, 7, 59. Prime factorization of 17346 in exponential form is:

17346 = 2¹ × 3¹ × 7² × 59¹

Step-2: Prime Factorization of 17360

Prime factors of 17360 are 2, 5, 7, 31. Prime factorization of 17360 in exponential form is:

17360 = 2⁴ × 5¹ × 7¹ × 31¹

Step-3: Factors of 17346

List of positive integer factors of 17346 that divides 17346 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 59, 98, 118, 147, 177, 294, 354, 413, 826, 1239, 2478, 2891, 5782, 8673

Step-4: Factors of 17360

List of positive integer factors of 17360 that divides 17346 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 31, 35, 40, 56, 62, 70, 80, 112, 124, 140, 155, 217, 248, 280, 310, 434, 496, 560, 620, 868, 1085, 1240, 1736, 2170, 2480, 3472, 4340, 8680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17346 and 17360. The biggest common factor number is the GCF number.
So the greatest common factor 17346 and 17360 is 14.

Also check out the Least Common Multiple of 17346 and 17360