Can a greatest common factor be 1?

2 Answers
Mar 28, 2016

Answer:

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# .

Aug 26, 2016

Answer:

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.