Question

Explain the reason why \[3\times 5\times 7+7\] is a composite number.

Answer 1

Hint: In this question we can represent the final answer as the multiple of the product of prime numbers to show the number as a composite number. The opposite of prime numbers is composite numbers. Using this fact explains the required answer.

Complete step-by-step answer:

The given number is: \[3\times 5\times 7+7\].

Any non-prime number which can be represented as the multiple of the product of prime numbers is known as composite number. We have ‘1, 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 43’ and so on. Prime numbers are numbers which can be divided by either 1 or the number itself.

From the BODMAS rule, we know the priority of the mathematical operators to use in an expression. B – Brackets, means we need to solve all the expressions in the brackets on first priority.
O – Open, means after solving the brackets’ expressions we need to open the brackets results/expressions and apply the suitable operators for multiplication or positive/negative signs as per situation.
Then, D – Division, M- Multiplication, A - Addition and S - Subtraction comes in the descending priority list.

Now here in question, we have only multiplications and additions.
We will first do the multiplications and then the addition in the given expression as per BODMAS rule.
$\begin{align}
  & 3\times 5\times 7+7 \\
 & =15\times 7+7 \\
 & =105+7 \\
 & =112 \\
\end{align}$

Now $112$ can be represented as the multiple of:
$16\times 7$ or $2\times 2\times 2\times 2\times 7$
So, we can see that 112 is a product of prime number 7 and 2.

Hence, \[3\times 5\times 7+7\] is a composite number as it is a product of prime numbers.

Note: There is possibility of mistake when not following the BODMAS rule and doing the addition before the multiplication. When addition is done before multiplication, we get an answer as 210 instead of 112. The function priority must be kept in consideration.