What is the Greatest Common Factor of 17 and 34?

Greatest common factor (GCF) of 17 and 34 is 17.

GCF(17,34) = 17

We will now calculate the prime factors of 17 and 34, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17 and 34.

How to find the GCF of 17 and 34?

We will first find the prime factorization of 17 and 34. After we will calculate the factors of 17 and 34 and find the biggest common factor number .

Step-1: Prime Factorization of 17

Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:

17 = 17¹

Step-2: Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:

34 = 2¹ × 17¹

Step-3: Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

Step-4: Factors of 34

List of positive integer factors of 34 that divides 17 without a remainder.

1, 2, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17 and 34. The biggest common factor number is the GCF number.
So the greatest common factor 17 and 34 is 17.

Also check out the Least Common Multiple of 17 and 34