How do you find the greatest common factor of 34 and 45?

34=2x17, both of these are prime numbers As 45 is not divisible by either 2 or 17, the greatest number which is a factor of both is 1

To find the greatest common factor (GCF) of 34 and 45, you can use various methods such as prime factorization, listing factors, or the Euclidean algorithm. One efficient method is to use the Euclidean algorithm, which involves finding the remainder when one number is divided by the other repeatedly until you reach a remainder of 0. The GCF is the divisor when the remainder becomes 0.

Using the Euclidean algorithm:

[ \text{Step 1:} \quad \text{Divide the larger number by the smaller number and find the remainder.} ] [ \text{Step 2:} \quad \text{Replace the larger number with the smaller number and the smaller number with the remainder.} ] [ \text{Step 3:} \quad \text{Repeat steps 1 and 2 until the remainder is 0. The divisor at this point is the GCF.} ]

Applying this to 34 and 45:

[ \text{Step 1:} \quad 45 = 34 \times 1 + 11 ] [ \text{Step 2:} \quad 34 = 11 \times 3 + 1 ] [ \text{Step 3:} \quad 11 = 1 \times 11 + 0 ]

So, the remainder is 0 at the third step, and the divisor at this point is 1. Therefore, the greatest common factor of 34 and 45 is 1.