Question

Look at the digits 36, 42, 54, 28, 84 and 77: a. Write down all the numbers which have 6 as a factor.

Answer 1

Given the numbers:

36, 42, 54, 28, 84, 77

A number has 6 as a factor if it ends in 0, 2, 4, 6, or 8, and if the sum of all the digits is a multiple of 3.

Only 77 do not meet the first condition. Now, we add the digits:

$\begin{gathered} 36\colon3+6=9=3\cdot3\text{ (Second condition)} \\ 42\colon4+2=6=3\cdot2\text{ (Second condition)} \\ 54\colon5+4=9=3\cdot3\text{ (Second condition)} \\ 28\colon2+8=10=5\cdot2 \\ 84\colon8+4=12=3\cdot4\text{ (Second condition)} \end{gathered}$

The numbers which have 6 as a factor are:

36, 42, 54, 84