Question

Find the GCF (34, 85)

Answer 1

Finding GCF for 34 and 85 using all factors (divisors) listing

The first method to find GCF for numbers 34 and 85 is to list all factors for both numbers and pick the highest common one:

All factors of 34: 1, 2, 17, 34

All factors of 85: 1, 5, 17, 85

So the Greatest Common Factor for 34 and 85 is 17

Finding GCF for 34 and 85 by Prime Factorization

The second method to find GCF for numbers 34 and 85 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 34: 2, 17

All Prime Factors of 85: 5, 17

As we can see there is only one Prime Factor common to both numbers. It is 17. So 17 is the Greatest Common Factor of 34 and 85

Answer 2

To find the greatest common factor (GCF) of 34 and 85, we can use the Euclidean algorithm:

85 = 2 × 34 + 17
34 = 2 × 17 + 0

Since we have reached a remainder of 0, the GCF of 34 and 85 is the divisor in the second-to-last line, which is 17.

Therefore, the GCF of 34 and 85 is 17.