Question

The gcf of two numbers is 170. neither number is divisible by the other. what is the smallest these two numbers could be? (prime factorization of 170 = 2 x x 5 x 17)

please help!!

Answer 1

The smallest possible numbers with a greatest common factor (GCF) of 170 are 10 and 17.

Step-by-step explanation:

To find the smallest possible numbers with a greatest common factor (GCF) of 170, we need to consider the prime factorization of 170, which is 2 x 5 x 17. Since neither number is divisible by the other, we can set up the two numbers as 2 x 5 x A and 17 x B, where A and B are the remaining prime factors. To find the smallest numbers, we choose the smallest possible values for A and B.

Therefore, the smallest possible values for the two numbers are:

1. 2 x 5 x 1 = 10
2. 17 x 1 = 17

So, the smallest numbers with a GCF of 170 are 10 and 17.

Answer 2

`340`

Step-by-step explanation:

Given: GCF of two numbers is
`170`. neither number is divisible by the other.

To Find: smallest of these two number.

Solution:

As GCF of two numbers is
`170`, both number are divisible by
`170`.

Prime factor of
`170`
`=2*5*17`

multiples of
`170` are
`1*2*5*17=170`

`2*2*5*17=340`

`3*2*5*17=510`

GCF of all three multiples is
`170`,

Here
`340` and
`510` are the two multiples whose GCF is
`170` and neither is divisible by other

Hence the smallest of two is
`340`, the answer is
`340`