What is the Greatest Common Factor of 17705 and 17719?

Greatest common factor (GCF) of 17705 and 17719 is 1.

GCF(17705,17719) = 1

We will now calculate the prime factors of 17705 and 17719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17705 and 17719.

How to find the GCF of 17705 and 17719?

We will first find the prime factorization of 17705 and 17719. After we will calculate the factors of 17705 and 17719 and find the biggest common factor number .

Step-1: Prime Factorization of 17705

Prime factors of 17705 are 5, 3541. Prime factorization of 17705 in exponential form is:

17705 = 5¹ × 3541¹

Step-2: Prime Factorization of 17719

Prime factors of 17719 are 13, 29, 47. Prime factorization of 17719 in exponential form is:

17719 = 13¹ × 29¹ × 47¹

Step-3: Factors of 17705

List of positive integer factors of 17705 that divides 17705 without a remainder.

1, 5, 3541

Step-4: Factors of 17719

List of positive integer factors of 17719 that divides 17705 without a remainder.

1, 13, 29, 47, 377, 611, 1363

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17705 and 17719. The biggest common factor number is the GCF number.
So the greatest common factor 17705 and 17719 is 1.

Also check out the Least Common Multiple of 17705 and 17719