Question

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

Answer 1

Solution:

A prime number is a number that has exactly two factors i.e. $1$ and number itself.

Prime numbers less than $20$ are $2,3,5,7,11,13,17$ and $19$.

Five pairs of prime numbers less than $20$ whose sum is divisible by $5$ are shown below,

$$\begin{gathered} a.(2,3)\mathrm{because}2+3=5\mathrm{and}5÷5=1 \\ \mathrm{b}.(2,13)\mathrm{because}2+13=15\mathrm{and}15÷5=3 \\ \mathrm{c}.(3,17)\mathrm{because}3+17=20\mathrm{and}20÷5=4 \\ \mathrm{d}.(7,13)\mathrm{because}7+13=20\mathrm{and}20÷5=4 \\ \mathrm{e}.(11,19)\mathrm{because}11+19=30\mathrm{and}30÷5=6 \end{gathered}$$

Hence, the five pairs of prime numbers less than $20$ whose sum is divisible by $5$ are $(2,3),(2,13),(3,17),(7,13)\mathrm{and}(11,19)$.