Question

Check whether the given numbers are divisible by $7$ or not?
A. $427$
B. $3514$
C. $861$
D. $4676$

Answer 1

Hint: First, we will define what divisibility rules are. Then we will write down the rule for divisibility by $7$, then we will check each option with the divisibility rule which we wrote down earlier and then at the end we will write which options satisfy the rule and get the answer.

Complete step by step answer:
Now, let’s define what is meant by the divisibility rule. Divisibility tests or division rules help one to check whether a number is divisible by another number without the actual method of division. If a number is completely divisible by another number that means the quotient will be a whole number and the remainder will be zero. Since every number is not completely divisible by every other number such numbers leave remainder other than zero.
Now, let’s see the rule for divisibility by $7$. For this rule, we will first remove the last digit of the number and double it, then subtract it from the remaining number if the number obtained is $0$ or recognizable $2$ digit multiple of $7$ for example: $14,21,28,35$ etc. then it is divisible by $7$ , now if the obtained number is not a recognizable $2$ digit multiple of $7$ then we will again follow this process until the number obtained either multiple of $7$ or some other number.
Let’s take the first option that is $427$ :
Now from the rule stated remove the last digit from the number that is $7$ and double it, which becomes $14$ .
Now the remaining number is $42$ , so we will subtract $14$from $42$ that is: $42-14=28$ , now we know that $28$ is a multiple of $7$.
Therefore, option A that is $427$ is divisible by $7$.
Now we will take the second option that is $3514$ :
Now from the rule stated remove the last digit from the number that is $4$ and double it, which becomes $8$ .
Now remaining number is $351$ , so we will subtract $8$from $351$ that is: $351-8=343$ , now the obtained number is not a recognizable two digit multiple of $7$ then we will again follow the process, so now we will again remove the last digit from the number that is $3$ , now after doubling it we will get: $6$.
Now the remaining number is $34$ , so we will subtract $6$ from $34$ that is: $34-6=28$ , now we know that $28$ is a multiple of $7$.
Therefore, option B that is $3514$ is divisible by $7$.
Now, let’s take the third option that is $861$ :
Now from the rule stated remove the last digit from the number that is $1$ and double it, which becomes $2$ .
Now the remaining number is $86$ , so we will subtract $2$ from $86$ that is: $86-2=84$ and it will be divisible by $7$.
Therefore, option C that is $861$ is divisible by $7$.
Finally, we will take the fourth option that is $8676$ :
Now from the rule stated remove the last digit from the number that is $6$ and double it, which becomes $12$ .
Now remaining number is $867$ , so we will subtract $12$ from $867$ that is: $867-12=855$ , now the obtained number is not a recognizable two digit multiple of $7$ then we will again follow the process, so now we will again remove the last digit from the number that is $5$ , now after doubling it we will get: $10$.
The remaining number is $85$ , so we will subtract $10$ from $85$ that is: $85-10=75$ , now the obtained number is not a recognizable two digit multiple of $7$.
Therefore, option D that is $8676$ is not divisible by $7$.

Hence, option A,B,C is divisible by $7$ and D is not divisible by $7$.

Note: Remember that when a number is divisible by another number, it is also divisible by the factors of the number, for example if $48$ is divisible by $12$ and we know that $12=4\times 3\times 2$ , so $2,3\text{ and }4$ are the factors of $12$ . Therefore: $48$ is also divisible by $2,3\text{ and }4$.