Question

How do you write 24 as a product of prime factors?

Answer 1

Hint: To obtain the prime factors of a given number we will use prime factorization. Firstly we will find the prime factor of 24 by using a long division method then we will simplify the factors by adding the power of factor with the same base and get the desired answer.

Complete step by step answer:
We have to find prime factors of:
$24$…..$\left( 1 \right)$
We will use prime factorization method which is long division as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1 \\
\end{align}$
So we can write equation (1) as below:
$24=2\times 2\times 2\times 3$
Now we will add the power of factor with same base and simplify it as below
$24={{2}^{3}}\times 3$
So we get the prime factors of 24 as $2\times 2\times 2\times 3$ or ${{2}^{3}}\times 3$
Hence we can write 24 as a product of prime factors as $2\times 2\times 2\times 3$

Note: Prime numbers are those which are divisible by 1 and itself only. Prime factors of a number are the values that divide the number completely and are also a Prime number. Prime factorization technique is used to find the prime factors of a number which when multiplied gives the number back. This method is only applicable to composite numbers and not prime numbers. We use this method to find out the HCF (Highest Common Factor) and LCM (Least Common Multiple) of any given set of numbers. There are two methods to find the prime factors of a number known as Division method and Factor Tree method. Division method is mostly used as it is less complicated and only requires easy calculation.