Realise that 30 = 6 x 5

Since number ÷ 30 = quotient R8,

Then number = 30 x quotient + 8

Since 30 = 6 x 5 ,

Number = 6 x 5 x quotient + 8
= 6 x (5 x quotient) + 8

From here we can see that because 30 is a multiple of 6, the (quotient x 30) is a multiple of 6 as well


To make the number divisible by 6, we add a number such that the 8 increases to a multiple of 6.

Realise that the closest multiple of 6 that is bigger than 8 , is 12 as 12 = 6 x 2

So 12 - 8 = 4

We add 4

Already, 30 is a multiple of 6.
but remainder 8 is not a multiple of 6.
to make remainder a multiple of 6,
what no. do we add to 8?
ans: 4
bcos 8+4 = 12 , a multiple of 6.