Question

A natural number N when divided by $12$ leaves a remainder of $7$. Find the remainder when N is divided by $6$.

Answer 1

Hint: Here, we will use the Using the Division Algorithm which states that – dividend is equal to the product of the divisor and the quotient and the sum of its value with the remainder. First of all convert the given word statement in the mathematical expression and then will find the required value using the first equation so formed.

Complete step by step solution:
Given that: A natural number N when divided by $12$ leaves a remainder of $7$.
Let us assume “q” to be the quotient.
Using the Division Algorithm which states that –Dividend $ = $Divisor $ \times $Quotient $ + $Remainder
Then the Number will be $N = 12q + 7$
The above equation can be re-written as,
$N = 12q + 6 + 1$
Make the pair of two first terms
$N = \underline {12q + 6} + 1$
Find the common multiples in the above expression,
$N = 6(2q + 1) + 1$
Now, when the above expression is divided by the number the remainder is exactly the number $1$
Hence, the remainder when $N$ is divided by $6$ is $1$.

Note:
At least remember the multiples till twenty. Be good in multiples and the division to use the division algorithm theorem. Always cross check the dividend once the division is performed to verify that the resultant quotient and the remainder are correct.