Question

What is the prime factorization of the number $ 8,788 $ ?

Answer 1

Hint: In this question, we need to find the prime factors of $ 8,788 $ . Here, we will be required to do a prime factorisation of $ 8,788 $ and thus determine all the prime factors of $ 8,788 $ . Prime factorization is a method of finding prime numbers which multiply to make the original number.

Complete step-by-step answer:
Here, we need to do a prime factorisation of $ 8,788 $ .
We know that $ 8,788 $ is a composite number.
As a result of doing the prime factorisation, we get to find all the prime factors of the number given to us in the problem itself.
A prime number is a natural number greater than $ 1 $ that is not a product of two smaller natural numbers.
In prime factorization, we start dividing the number by the first prime number $ 2 $ and continue to divide by $ 2 $ until we get a decimal or remainder. Then divide by $ 3,5,7,.... $ etc. until we get the remainder $ 1 $ with the factors as prime numbers. Then write the numbers as a product of prime numbers.
Thus, prime factorization of $ 8,788 $ is,
 $ 8,788 = 2 \times 2 \times 13 \times 13 \times 13 $
This can be also written in exponential form as:
 $ 8,788 = {2^2} \times {13^3} $
So, the correct answer is “ $ 8,788 = {2^2} \times {13^3} $ ”.

Note: In this question it is important to note here that a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $ 1 $ and itself. However, the prime factorization is also known as prime decomposition. And, the prime factorization of the prime number is the number itself and $ 1 $ . Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers.