What is the Greatest Common Factor of 17105 and 17120?

Greatest common factor (GCF) of 17105 and 17120 is 5.

GCF(17105,17120) = 5

We will now calculate the prime factors of 17105 and 17120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17105 and 17120.

How to find the GCF of 17105 and 17120?

We will first find the prime factorization of 17105 and 17120. After we will calculate the factors of 17105 and 17120 and find the biggest common factor number .

Step-1: Prime Factorization of 17105

Prime factors of 17105 are 5, 11, 311. Prime factorization of 17105 in exponential form is:

17105 = 5¹ × 11¹ × 311¹

Step-2: Prime Factorization of 17120

Prime factors of 17120 are 2, 5, 107. Prime factorization of 17120 in exponential form is:

17120 = 2⁵ × 5¹ × 107¹

Step-3: Factors of 17105

List of positive integer factors of 17105 that divides 17105 without a remainder.

1, 5, 11, 55, 311, 1555, 3421

Step-4: Factors of 17120

List of positive integer factors of 17120 that divides 17105 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 107, 160, 214, 428, 535, 856, 1070, 1712, 2140, 3424, 4280, 8560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17105 and 17120. The biggest common factor number is the GCF number.
So the greatest common factor 17105 and 17120 is 5.

Also check out the Least Common Multiple of 17105 and 17120