Question

Using euclid's division algorithm, show that only one of the numbers n, n+2, n+4 is divisible by three

Answer 1

Hi friend,

Given numbers,

n, n+2 and n+4

'n' is any positive integer.

If n = 1,

n = 1
n+2= 1+2 = 3 is divisible by 3
n+4 = 1+4 =5

If n = 2,

n = 2
n+2 = 2+2 = 4
n+4 = 2+4 = 6 is divisible by 3.

If n = 3,

n = 3 is divisible by 3.
n+2 = 3+2=5
n+4 = 3+4=7

From this observation, it is clear that one and only one out of n, n+2 and n+4 is divisible by 3.