What is the Greatest Common Factor of 17346 and 17353?

Greatest common factor (GCF) of 17346 and 17353 is 7.

GCF(17346,17353) = 7

We will now calculate the prime factors of 17346 and 17353, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17346 and 17353.

How to find the GCF of 17346 and 17353?

We will first find the prime factorization of 17346 and 17353. After we will calculate the factors of 17346 and 17353 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 17353

Prime factors of 17353 are 7, 37, 67. Prime factorization of 17353 in exponential form is:

17353 = 7¹ × 37¹ × 67¹

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 17353

List of positive integer factors of 17353 that divides 17346 without a remainder.

1, 7, 37, 67, 259, 469, 2479

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17346 and 17353. The biggest common factor number is the GCF number.
So the greatest common factor 17346 and 17353 is 7.

Also check out the Least Common Multiple of 17346 and 17353