Chapter SR4, Problem 7P

Solution

The prime factorization of the number $72$ .

  $2\cdot 2\cdot 2\cdot 3\cdot 3\text{ or }{2}^3\cdot 3^2$

Given:

The number $72$ .

Concept Used:

Prime factorization of a number is writing a number as a product of prime numbers, where prime numbers are natural number greater than 1 whose have no other factor than 1 and itself.

Calculation:

In order to write the prime factorization of the number $72$ , divide the number starting with least prime factors until there is no more composite factors as shown below

  $\begin{array}{l}72\\ \swarrow \searrow \\ \text{ 2 }\cdot \text{ 36}\\ \swarrow \searrow \\ \text{ 2 }\cdot \text{ 18}\\ \swarrow \searrow \\ \text{ 2 }\cdot \text{ 9}\\ \swarrow \searrow \\ \text{ 3 }\cdot \text{ 3}\end{array}$

Thus, the prime factorization of $72$ is $2\cdot 2\cdot 2\cdot 3\cdot 3\text{ or }{2}^3\cdot 3^2$ .