Question

What is the prime factorization of \[231\]?

Answer 1

Hint: In the given question, we are asked to find the prime factorization of the given number \[231\]. Prime factorization refers to a process in which we write any given number as the product of prime numbers only. We will first divide by the smallest prime number which can divide the given number, so we will take 3 first. We get, \[231=3\times 77\], that is, we will get the quotient as 77. We will continue dividing the quotient by the smallest prime number possible, so we will now take 7. We have, \[77=7\times 11\]. Therefore, we will have the factorization of the given number consisting of only prime numbers.

Complete step-by-step answer:
According to the given question, we are given a number whose prime factorization we have to find.
Prime factorization refers to a process in which we write any given number as the product of prime numbers only. In this we follow a simple rule. We have to divide the given number by the smallest prime number which can divide that number and then we will get a quotient. We will repeat the same procedure with the quotient. The process is continued until all the factors are prime numbers only.
The number given to us is,
\[231\]
The smallest prime number that can divide the given number is 3. On division we get the quotient as 77, that is,
\[231=3\times 77\]
Here, 3 is a prime number but 77 is a composite number. We will now divide 77 by the smallest possible prime number. We have,
\[77=7\times 11\]
Here, both 7 and 11 are prime.
Therefore, the prime factorization of the given number is, \[231=3\times 7\times 11\].

Note: Prime numbers are those which have the multiples as 1 and the number itself. For example – 3 is a prime number as, \[3=1\times 3\]. Another set of numbers that we have is composite numbers. Composite numbers are those numbers which have other multiples along with 1 and the number itself. For example – 6 is a composite number as its factors are, \[6=2\times 3\]. While solving the question, the prime numbers and the composite numbers should not be confused with.