Question

Write all the factors of 98.

Answer 1

Hint: We first describe the process of finding the prime factorisation and the long division. Using the division, we find the least prime which divides the given number. At the end we take the multiplied form to find the factors.

Complete step-by-step answer:
The process of finding the factors of a number is to find the smallest prime possible which divides the number. We complete the division then look for the same process again. We continue this process until we get 1 as the remaining quotient.
Therefore, if we need the prime factorisation of $a$ and we find $x$ to be the least prime that divides $a$, then we take $\dfrac{a}{x}$ for the next step and find its least prime factor to continue the process.
At the end we write the factors in multiplied form.
For our given 98, we find the prime factorisation using long division.
\[\begin{align}
  & 2\left| \!{\underline {\,
  98 \,}} \right. \\
 & 7\left| \!{\underline {\,
  49 \,}} \right. \\
 & 7\left| \!{\underline {\,
  7 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Therefore, the prime factorisation of 98 is $98=2\times 7\times 7$.
The factors of the 98 are 1, 2, 7, $2\times 7=14$, $7\times 7=49$, $2\times 7\times 7=98$.
So, the correct answer is “ 1, 2, 7, 14, 49, 98$”.

Note: We need to be careful about taking the factors only as primes. We can’t take composite numbers for the division. We can find the number of primes from the formula of $\left( m+1 \right)\left( n+1 \right)\left( p+1 \right)$ for the prime factorisation $x={{a}^{m}}{{b}^{n}}{{c}^{p}}$.