Can a greatest common factor be 1?

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Answer 1 · 2016-03-28T22:29:25

Yes

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 · 2016-08-26T00:24:29

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

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.