SOLUTION: how to show that a is relatively prime to n

Question 697847: how to show that a is relatively prime to n
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You need to show that they do not have any prime factors in common.
For that you need to write the prime factorization of each number.
and

are relatively prime to each other.
Each can only be divided by products of its prime factors,
but since they have no common prime factors, their greatest common divisor is .

On the other hand,
and

are not relatively prime to each other,
because they both have in common and as prime factors,
so both can be divided by .
RELATED QUESTIONS
For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than... (answered by ikleyn,math_tutor2020)

Show that 5n+3 and 7n+ 4 are relatively prime for all... (answered by khwang)

Two positive integers M and N are defined to be relatively prime if GCF(M, N) = 1.... (answered by consc198,math_iz_hard)

Let a not equal 0, b and c be integers with a and b relatively prime. Show that if a|b*c (answered by venugopalramana)

Let a and b be relatively prime intergers and let k be any integer. Show that b and a+bk... (answered by richard1234)

Show that 165,342,985 and 13 are relatively... (answered by vleith)

Show that 83,154,367 and 4 are relatively... (answered by ikleyn)

how many positive integers less than or equal to 70,are relatively prime... (answered by nabla)

How many numbers less than 20 are relatively prime to 20... (answered by Naveen11)