Question

How do you find the prime factorization of 72?

Answer 1

Hint:
In the given question, we have been asked to find the prime factorization of a natural number. For doing that, we divide the given number by its smallest factor. If it is not divisible by that factor then we move onto the next smallest factor, but if it is, then we divide it by the smallest factor till it is no longer divisible by that factor. And we repeat the same steps for all the factors.

Complete Step by Step Solution:
The given number is \[72\].
We can easily solve it by using prime factorization,
\[\begin{array}{l}2\left| \!{\underline {\,
  {72} \,}} \right. \\2\left| \!{\underline {\,
  {36} \,}} \right. \\2\left| \!{\underline {\,
  {18} \,}} \right. \\3\left| \!{\underline {\,
  9 \,}} \right. \\3\left| \!{\underline {\,
  3 \,}} \right. \\{\rm{ }}\left| \!{\underline {\,
  1 \,}} \right. \end{array}\]
Hence, \[72 = 2 \times 2 \times 2 \times 3 \times 3 = {2^3} \times {3^2}\]

\[72 = 2 \times 2 \times 2 \times 3 \times 3 = {2^3} \times {3^2}\]

Additional Information:
While the number of factors of a number is limited, i.e., at one point, the list of factors ends, or we can say, the list of factors is exhaustive. But the number of multiples of a number is infinite. This is because the counting never ends, and by multiplying any number, we get one number more in the set of multiples.

Note:
For solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we think about the concept or formula which contains the known and the unknown and pick the one which is the most suitable and the most effective for finding the answer of the given question. Then we use the results or finding of the concept and apply it to our question. It is really important to know and follow all the results of the concepts if we have to solve the question correctly, as one slightest error gives the incorrect result.