Question

Any number that is divisible by 3 is also divisible by 9.

Find a counterexample to show that the conjecture is false.
18
27
45
48

Answer 1

`48\ is\ divisible\ by\ 3\ but\ isn't\ divisible\ by\ 9:\\\\48:3=16\\\\48:9=5(3)/(9)=5(1)/(3)\\\\Other\ examples:\\\\51:3=17;\ 51:9=5(2)/(3)\\\\6:3=2;\ 6:9=(2)/(3)\\\vdots`

Answer 2

For a number to be divisible by 9 the sum of the digits is also divisible by 9.
For the examples given 48 (4+8 = 12) (1 + 2 = 3) therefore 48 is not divisible by 9 as the sum of the digits is 3.

For a number to e divisible by 3 the sum of the digits is also divisible by 3. (eg 48 (4+8 = 12), (1 + 2 = 3) therefore 48 is divisible by 3