Can a greatest common factor be 1?

Question

Benjamin Altschul · Accepted Answer

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

Other than one, numbers like 24 and 35 have nothing in common. The following are their primary factors: #24 = 2xx2xx2xx3# #35= color(white)(xxxxxxxxxx)5xx7# The HCF in this scenario would be 1. Every number has a factor of 1.

Nova Allen · Answer

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# .

Zoe Adams · Answer

undefined Yes, the greatest common factor (GCF) of two numbers can be 1. This occurs when the numbers do not share any common factors other than 1. In other words, if the only positive integer that divides both numbers evenly is 1, then the GCF of those numbers is 1. This often happens when the numbers are relatively prime, meaning they have no common factors other than 1. For example, the GCF of 6 and 7 is 1, as the only positive integer that divides both 6 and 7 evenly is 1. Similarly, the GCF of 15 and 28 is also 1, as 15 and 28 do not share any common factors other than 1.