Question

What are the factors of 29?

Answer 1

Hint: The factors of 29 are going to found by factoring this 29 which is accomplished by hit and trial method in which we try to divide 29 by 2 if it got completely divisible by 2 then we write the quotient and then by hit and trial method try to divide the quotient by checking the divisibility by 2, 3… and so on. This procedure will continue will we get the quotient as 1.

Complete step-by-step answer:
In the above problem, we are asked to find the factors of 29. For that, we are going to divide 29 by a number in such a way so that 29 will get completely divided. As the last number of 29 is not an even number so 57 won’t get divided by 2 and the divisibility rule for 3 is not applicable because the sum of the numbers (2 and 9) is 11 and 11 is not completely divisible by 3. Similarly, 5 is also not divisible by 29 because it has no 5 in the unit digit of 29. In this way, by checking the divisibility rule for other numbers you will find that 29 is only divisible by 29 and we get,
Dividing 29 by 29 we get,
$\begin{matrix}
   29 \\
   {} \\
\end{matrix}\left| \!{\overline {\,
 \begin{align}
  & 29 \\
 & 1 \\
\end{align} \,}} \right. $
And we know that a prime number is a number which has only 2 factors 1 and the number itself so 29 is a prime number.
Hence, the factors of 29 are 29 and 1.

Note: If in the above problem, instead of asking the factors of 29, they would ask the prime factors for 29 then 29 is the only factor because 1 is not a prime number. This is the mistake which could possibly happen.