Using set theory prove that the following pairs of numbers are prime to each other.
a) 15,24 b)30,49
Solution:
(i) factors of 15, set A = { 3 ,5,15}
factors of 24, set B = { 2,3,4,6,8,12,24 }
Since, ( A n B) = {3}
So , 15 and 24 are not prime to each other.
(ii) factors of 30 ,Set A={2,3,5,6,10,15,30}
factors of 49 , Set B= {7,49 }
since, (A n B ) = phie or Null set
(i) factors of 15, set A = { 3 ,5,15}
factors of 24, set B = { 2,3,4,6,8,12,24 }
Since, ( A n B) = {3}
So , 15 and 24 are not prime to each other.
(ii) factors of 30 ,Set A={2,3,5,6,10,15,30}
factors of 49 , Set B= {7,49 }
since, (A n B ) = phie or Null set
So , A and B are relative primes