Question

How do you write $ 1386 $ as the product of its prime factors?

Answer 1

Hint: In order to express the given number as the product of its prime factors, use the concept of prime factorisation and write all the prime factors and to simply the factors product apply the law of exponents as $ {a^m} \times {a^n} = {a^{m + n}} $ .

Complete step-by-step answer:
We are given a number $ 1386 $ which is composite in nature .
As per the question we have to express $ 1386 $ into the product of its prime factors.
We know the prime factorisation of a number is the representation of a number in terms of multiples of its factors.
In the prime factorisation of number $ 1386 $ , we got
 $ \Rightarrow 1386 = 2 \times 3 \times 3 \times 7 \times 11 $
Now to simplify the above factorisation by applying the exponent rule to make the prime factorisation simplest.
Law of exponents states that when the base of two numbers is same ,we can add the powers of that element i.e. $ {a^m} \times {a^n} = {a^{m + n}} $
 As we can see the prime factor 3 is coming 2 times , so using the exponent rule , we can rewrite the factorisation as
 $ \Rightarrow 1386 = 2 \times {3^2} \times 7 \times 11 $
So, the correct answer is “ $ \ 1386 = 2 \times {3^2} \times 7 \times 11 $ ”.

Note: Prime factorisation: it is a process of writing a number in multiples of its factors where all the factors are prime numbers.
1. Composite numbers are the whole numbers that have more than two factors. In other words all the whole numbers other than prime numbers are known as composite numbers.
2.Remember the law of exponents is only applicable when the base of two numbers having some exponent value is the same.
3.Make sure you write all the prime factors properly.