Question

Check whether 2156 is divisible by 11 and 7? Verify whether 2156 is divisible by product of 11 and 7 ?
[3 marks]

Answer 1

We know that, if the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
In 2156, (6 + 1) - (2 + 5) = 0
⇒ 2156 will be divisible by 11.
[1 mark]

Now, for divisibility by 7
$\begin{array}{cc}2& 156\end{array}$
Now, 156 - 2 = 154
Since, 154 is divisible by 7 as 154 ÷ 7 = 22.
Therefore, 2156 will also be divisible by 7.
[1 mark]

We know that if a number is divisible by $a$ and $b$, then it will be also divisible by $a\times b$. If $a$ and $b$ are coprime numbers.
Since, 7 and 11 are coprime number.
Hence, 2156 will also be divisible by product of 7 and 11.
[1 mark]