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

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: how to show that a is relatively prime to n      Log On


   

Question 697847: how to show that a is relatively prime to n
Answer by KMST(5328) About Me  (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.
630=2%2A3%5E2%2A5%2A7 and
143=11%2A13
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 1.

On the other hand,
630=2%2A3%5E2%2A5%2A7 and
165=3%2A5%2A11
are not relatively prime to each other,
because they both have in common 3 and 5 as prime factors,
so both can be divided by GCD%28630%2C165%29=3%2A5=15.