Question

Check whether 413 is divisible by 7 or not. If yes, the answer is 1 else 0.

Answer 1

Hint: We find out the concept of multiplier. If the given numbers are formed as a multiplication form of two positive whole numbers then we can assure about the divisibility. We also check whether it is directly divisible by 7 using the division formulas.

Complete step-by-step solution:
The concept of a number being divisible by another number comes from the concept of multiplicity which is the expression of the first number being termed as a multiplication form of two other positive whole numbers different from the given first number.
For the divisibility of 7, we know that we take twice the unit value. Then we subtract that value from the remainder of the original number. If that subtracted value is divisible by 7 then the number itself is divisible by 7.
For example, we take a number (pqr) where p, q, r are the digits in that number at the hundredth, tenth, unit places. So, we find r, take the twice of the digit which is 2r. The remainder of the number excluding the unit digit is (PQ). We subtract these two and if that value is divisible by 7 then we can say that (pqr) is divisible by 7. Take 2769. We take a unit digit and get twice of it which is $9\times 2=18$. Now, we take the subtraction of 18 from 276, the remaining of the number. We get $276-18=258$ which is not divisible by 7. So, 2769 is not divisible by 7 where $\dfrac{2769}{7}=395.57 $. If the number is very long then we can continue the same process as many times as we want.
Now we talk about 413. It has 3 in the unit place. The twice value is 6. So, the difference is $41-6=35$. It’s divisible by 7 as $\dfrac{35}{7}=5$. So, 413 is divisible by 7 where $\dfrac{413}{7}=59$.
So, 413 is divisible by 7.
We have been given instructions to end the answer as the binary commands.
Here the correct answer gives the result as 1 and the wrong answer gives the result as 0.
So, the answer is 1.

Note: We need to remember the theorems for the divisibility. If we can’t then there will be no way to find out other than doing long division. Using the theorem saves a lot of time. The multiplication form is also very important to establish the statement as true.