Question

What is the prime factorisation of 150?
A. $2\times 2\times 25$
B. $2\times 3\times 5\times 5$
C. $5\times 30$
D. $2\times 3\times 5$

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 prime factorisation of 150.

Complete step by step solution:
The process of finding the prime factorisation 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 prime in multiplied form to find the prime factorisation.
For our given 150, we find the prime factorisation using long division.
\[\begin{align}
  & 2\left| \!{\underline {\,
  150 \,}} \right. \\
 & 3\left| \!{\underline {\,
  75 \,}} \right. \\
 & 5\left| \!{\underline {\,
  25 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Therefore, the prime factorisation of 150 is $150=2\times 3\times 5\times 5$. So, the correct option is (B).

Note:
We need to be careful about taking the factors only as primes. We can’t take composite numbers for the division. We have to find the least prime and in the ascending order to smoothly complete the factorisation.