Number ÷ 6 = quotient R5
So number = 6 x quotient + 5


Number ÷ 8 = quotient R5
So number = 8 x quotient + 5

Realise that if we subtract 5 from the number , it is divisible by 6 or 8.

6 = 2 x 3
8 = 2 x 2 x 2


If a number is divisible by two numbers , it is divisible by the lowest common multiple of the numbers

Notice that 24 = 2 x 2 x 2 x 3
= 6 x 4 or 8 x 3

24 is the lowest common multiple of 6 and 8 as it contains only the prime factors of both numbers.


So the number is divisible by 24.we just find a multiple of 24 which when added to 5, is between 300 and 400.


Example :

24 x 15 = 360
360 + 5 = 365

Check : 365 ÷ 8 = 45 R5
365 ÷ 6 = 60 R5




Another way to think of this question :

If a number can be divided by 6, this means it can be split equally into groups of 6.

If a number can be divided by 8, this means it can be split equally into groups of 8.

Now 24 = 8 x 3
24 = 6 x 4

Among the groups of 6, we can combine every 4 groups to form bigger groups of 24.

Among the groups of 8, we can combine every 3 groups to form bigger groups of 24.


So it can also be divided equally by 24 since we can form groups of 24 with no remainder.