Question

What are the factors of 405?

Answer 1

Hint: In the given question we are asked to write the prime factors of the given number. We will write the factors and then check them whether they are prime or not. If not prime then we will verify all the factors of the non-prime number also.

Complete step-by-step answer:
According to the question we need to write the factor of the given number 405. Now, by factor we need to mention all those numbers which completely divide the given number 407.
Now, we can write 405 as $405=1\times 405$ . Also, 5 divides 405 so $405=5\times 81$ now we can see that 81 is the factor but it is not the prime factor so we must check that all the other factors of 81 must be the factor of 405. From 81 we have 3,9,27 and we are left to find the pairs.
$\begin{align}
  & 405=3\times 105 \\
 & 9\times 45 \\
 & 27\times 15 \\
\end{align}$
Now, we need to find the other factors $3\times 81=243$ is not the factor of the given number. Also, as soon as we reach the half number of the given number or the half way of the number after that we are left with no more factors. Now, the factors are {1,3,9,15,27,45,81,135,405}.

Note: While writing the factors of the number we must be aware that after the half of the number we can never get the factor of that number. Also, we must be careful while making the pairs and should also take care of the prime factor pairs rather than just using no prime factors also which may lead to wrong answers.