Question

Find the prime factorization of 32?

Answer 1

Hint: Here in this question we have been asked to prime factorize the given number 32. Factorisation is defined as expressing a number as a product of other numbers, or factors, which when multiplied together give the original number again. Prime factorization means to factorize using only prime numbers.

Complete step by step answer:
Now considering from the question we have been asked to prime factorize the given number 32.
From the basic concepts we know that the factorisation is defined as the expressing a number as a product of other numbers, or factors, which when multiplied together give the original number again and Prime factorization means factorize using only prime numbers.
Hence 32 can be written as $16\times 2$ . As 16 is not a prime number we need to further factorize it. By doing that we will get $\Rightarrow 2\times 2\times 8$ .
Similarly by factorization this expression further we will have $\Rightarrow 2\times 2\times 2\times 4=2\times 2\times 2\times 2\times 2$ . This process can be mathematically given as
 $\begin{align}
  & 2\left| \!{\underline {\,
  32 \,}} \right. \\
 & 2\left| \!{\underline {\,
  16 \,}} \right. \\
 & 2\left| \!{\underline {\,
  8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$ .

Therefore we can conclude that the factors of 32 are 1,2,4,8,16 and 32. The prime factored form of 32 is given as $2\times 2\times 2\times 2\times 2$

Note: While answering questions of this type we should be careful with the concepts that we apply and the calculations that we perform. Someone can ignore prime factorization and consider it as factorization which will lead them to answer the question as the factors of 32 are 1,2,4,8,16 and 32 which is a wrong conclusion.