Question

How do you write $84$ as a product of prime numbers?

Answer 1

Hint:As we know that prime numbers are those numbers that only have two or less factors, which are the number itself and the number $1$ . For example the numbers $1,2,3,5,7,$ etc are prime numbers. All of these numbers have only two factors. And prime factorisation refers to dividing numbers with prime numbers successively to find its prime factors.

Complete step by step solution:
As we have to write $84$ as a product of its prime numbers, so let’s find all the factors of $84$ first.
We can find factors of $84$ by multiplying their numbers to get the product i.e. $1*84 = 84,2*42 = 84,3*28 = 84$ and so on.
And the numbers can be further broken down. So all the factors of $84$ are $1,2,3,4,6,7,12,14,21,28,42,84$.
Now the factorisation: $84 \div 2 = 42 \Rightarrow 42 \div 3 = 21$ and further when $21$ is divided by $3$ it equals to $7$ and $7 \div 7 = 1$.
We can say that $84 = 2*2*3*7$ as these are the prime factors . Therefore $84 = {2^2}*3*7$.
Hence the prime factors of $84$ are ${2^2}*3*7$ .

Note: We have to keep in mind the difference between prime factors and normal factors. 2 is the smallest even prime number as it has only two factors that are $2,1$ only. Also $84$ is the sum of twin prime numbers i.e. $41$ and 43 . Here $84$ is a composite number which means it has more than $2$ factors.
And when a composite number is written as a product of its prime numbers , we have the prime factorisation of that number. Whole numbers that are not prime are composite numbers because of their factors.