Question

Express the following as a product of prime factor: \[182\]

Answer 1

Hint:We need to find the prime factors of the numbers. Remember the definition of prime numbers and by method of prime factorisation we get the required answer.

Complete step-by-step answer:
Prime Number: Any set of numbers which will only be divided by number \[1\] and itself. The smallest prime number is\[2\].
Prime factors: The factors of a number could be found out when divided by the prime numbers in the increasing order starting with\[2\].
We will proceed with the question but before doing that we need to be very clear about the concept of prime factorization and hence therefore we will follow the procedure.
Writing the data or information from the question and after doing so we will come to know that to find the prime factors $182$ we need to proceed with the concept as given in the hint section.
For finding prime factors of 182, simply divide the given number with the prime numbers and starting with the number 2 (which is also the smallest and only even prime number) after doing so we will obtain the number, which will then be divided by the suitable prime numbers and this cycle of division will be continued.
                 $$
                 \begin{array}{|l}
                \llap{2~~~~} 182 \\ \hline
                \llap{7~~~~} 91 \\ \hline
                \llap{13~~~~} 13 \\ \hline
                               3
                  \end{array}
               $$
Now we will, writing down the prime factors of $182$
$ \Rightarrow 182 = 2 \times 7 \times 13$
The prime factors of the given number $182$ is equal to $2,7$ and $13$.

Note:Such a question is of very easy level and only requires an introductory knowledge about the prime factors and the concept of the prime numbers is enough to solve questions of this type. Students generally commit mistakes in the factorization step where the division of a number by prime factors is done.