Almost a Million
Weekly Problem 26 - 2014
Which of the given numbers is divisible by 6?
Which of the given numbers is divisible by 6?
Age
11 to 14
Challenge level
Problem
Which of the following is divisible by 6?
(a) one million minus one
(b) one million minus two
(c) one million minus three
(d) one million minus four
(e) one million minus five
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: One million minus 4
Dividing by 6
$$\begin{align}166666&\text{ remainder 4}\\
6\overline{)1000000}&\end{align}$$ So $4$ less than $1000000$ is a multiple of $6$
Looking for multiples of 6
In order to be a multiple of 6, a number must be both even and a multiple of 3. Of the numbers given, only (b) 999 998 and (d) 999 996 are even.
For a number to be a multiple of 3, the sum of its digits must also be a multiple of 3. From this, we see that, of these two, only (d) 999 996 is a multiple of 3. Hence (d) is the only multiple of 6 here.