Question

Find the prime factorization of the number 450.

Answer 1

Hint: The prime factorization of any number means writing the number as a product of its prime factors. There should only be prime numbers in the factor. We can prime factorize any number by starting to divide it by the smallest possible prime number, that is, 2. If 2 is not a factor, then we move on to 3. If 3 is not a factor then we divide the number by next prime, that is 5 and so on. This is done until we get the quotient as 1.

Complete step by step solution:
The number given to us in the problem is equal to 450. We can prime factorize it by the method of “vertical” prime factorization method. In this method, the number is written on top. The prime factor of the number is written on the left side of this number and the resulting quotient is written just below. The sequence continues until we get the quotient as 1.
Now, calculating the prime factorization of 450 by aforesaid method, we get:
$\begin{align}
  & 2\left| \!{\underline {\,
  450 \,}} \right. \\
 & 3\left| \!{\underline {\,
  225 \,}} \right. \\
 & 3\left| \!{\underline {\,
  75 \,}} \right. \\
 & 5\left| \!{\underline {\,
  25 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & \left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$

Therefore 450 has been prime factorized and it can be written as a product of its factor in the following manner:
$\Rightarrow 450=2\times 3\times 3\times 5\times 5$
Hence, the prime factorization of the number 450 is equal to $2\times 3\times 3\times 5\times 5$.

Note: Whenever performing prime factorization of a number, we should always make sure all the divisors are prime factors only. Also, the final product of these factors should give us the original number. Here, the product of our prime factors, that is: $2\times 3\times 3\times 5\times 5$ is equal to 450 which is equal to the original number. Thus, our solution has been verified.