Question

Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

Answer 1

Hint: Prime numbers are natural numbers which have only two factors 1 and the number itself.

Set of prime numbers less than 20 are:
$\left( {2,3,5,7,11,13,17,19} \right)$
According to the given problem,
Pair of prime numbers less than 20, whose sum is divisible by 5 are:
$
  \left( i \right)\left( {2,3} \right)\left[ {\because 2 + 3 = 5} \right] \\
  \left( {ii} \right)\left( {3,7} \right)\left[ {\because 3 + 7 = 10} \right] \\
  \left( {iii} \right)\left( {2,13} \right)\left[ {\because 2 + 13 = 15} \right] \\
  \left( {iv} \right)\left( {7,13} \right)\left[ {\because 7 + 13 = 20} \right] \\
  \left( v \right)\left( {13,17} \right)\left[ {\because 13 + 17 = 30} \right] \\
 $
Since the sum of every set is divisible by 5.
Hence the pairs are $\left( {2,3} \right)\left( {3,7} \right)\left( {2,13} \right)\left( {7,13} \right)\left( {13,17} \right)$

Note:Any natural number which has only two factors i.e. 1 and the number itself called a prime number. In the above question we just did a combination of all prime numbers and tried for the sum of all the sets.