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Is $7*5*3*2+3$ a composite number? Justify your answer.

Last updated date: 22nd Jul 2024
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Hint: We solve this question by using the concepts of composite and prime numbers. A composite number is a whole number that has more than two factors. A prime number is one which has only two factors: 1 and the number itself.

Complete step by step answer:
We are required to find out if $7*5*3*2+3$ a composite number or not. To show it is a composite number, we are required to show that it has more than two factors. Let us consider the given number,
$\Rightarrow 7*5*3*2+3$
Since the first and second terms both have a 3 in common, let us take that out common.
$\Rightarrow 3\left( 7*5*2+1 \right)$
Taking a product of the terms in the brackets,
$\Rightarrow 3\left( 70+1 \right)$
Adding the two terms in the brackets,
$\Rightarrow 3\left( 71 \right)$
Taking a product of these two numbers,
$\Rightarrow 213$
Now, since this number has more than two factors as seen in the above step which shows that it can be obtained by taking a product of 3 and 71. It can also be obtained by multiplying 1 and 213. Hence, the number is a composite number as it does not have only two factors. It has four factors.
Looking at the above reasons, we can say that 213 is a composite number and not a prime number.

Note: We need to know the concept of prime and composite numbers to solve such problems. As we can see, a number cannot be both prime and composite at the same time. A prime number is one that is not divisible by any number other than 1 and itself. For such problems, we need to find out the factors of the given number. If it is more than one, it is a composite number.