Question

Can a greatest common factor be 1?

Answer 1

Yes

Explanation:

For example, let `X={p_1,p_2,....,p_n}` be a set of prime numbers.

Then `AA p_i in X, 1|p_i and p_i|p_i` .

That is, the only 2 factors of `p_i` is `1` and itself, `AAi=1,2,....,n`.

Since `p_i` is prime for all `i,=>p_` does not divide into `p_j AA i!=j`.

Therefore, `HCF(p_1,p_2,....,p_n)=1` .

Answer 2

It is easily possible to have only 1 as a common factor.

Explanation:

Numbers such as 24 and 35 do not have any common factor apart from 1.

Their prime factors are as shown:

`24 = 2xx2xx2xx3`
`35= color(white)(xxxxxxxxxx)5xx7`

In this case the HCF would be 1.

1 is always a factor of every number.