What is the Greatest Common Factor of 17355 and 17360?

Greatest common factor (GCF) of 17355 and 17360 is 5.

GCF(17355,17360) = 5

We will now calculate the prime factors of 17355 and 17360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17355 and 17360.

How to find the GCF of 17355 and 17360?

We will first find the prime factorization of 17355 and 17360. After we will calculate the factors of 17355 and 17360 and find the biggest common factor number .

Step-1: Prime Factorization of 17355

Prime factors of 17355 are 3, 5, 13, 89. Prime factorization of 17355 in exponential form is:

17355 = 3¹ × 5¹ × 13¹ × 89¹

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 17355

List of positive integer factors of 17355 that divides 17355 without a remainder.

1, 3, 5, 13, 15, 39, 65, 89, 195, 267, 445, 1157, 1335, 3471, 5785

Step-4: Factors of 17360

List of positive integer factors of 17360 that divides 17355 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 17355 and 17360. The biggest common factor number is the GCF number.
So the greatest common factor 17355 and 17360 is 5.

Also check out the Least Common Multiple of 17355 and 17360