Question

Check whether the given numbers are divisible by $7$ or not ?
(a) $427$ (b) $3514$ (c) $861$ (d) $4676$

Answer 1

For divisible by $7$: To check if a number is evenly divisible by $7$ take the last digit of the number, double it and then subtract the result from the rest of the number. If the resulting number is evenly divisible by $7$, so is the original number.
The Rule is to be applied as follows
(a) $427\Rightarrow 42-(7\times 2)=28$ which is divisible by $7$.
Therefore, number is divisible by $7$.
(b) $3514\Rightarrow 351-(4\times 2)=343$

Now, Further applying the same rule $34-(3\times 2)=28$ which is divisible by $7$.
Therefore, number is divisible by $7$.
(c) $861\Rightarrow 86-(1\times 2)=84$ which is divisible by $7$.
Therefore, number is divisible by $7$.
(d) $4676\Rightarrow 467-(6\times 2)=455$

Now, Further applying the same rule $45-(5\times 2)=35$ which is divisible by $7$.
Therefore, number is divisible by $7$.