Chapter SR4, Problem 10P

Solution

The prime factorization of the number $100$ .

  $2\cdot 2\cdot 5\cdot 5\text{ or }{2}^2\cdot 5^2$

Given:

The number $100$ .

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 $100$ , divide the number starting with least prime factors until there is no more composite factors as shown below

  $\begin{array}{l}100\\ \swarrow \searrow \\ \text{ 2 }\cdot \text{ 50}\\ \swarrow \searrow \\ \text{ 2 }\cdot \text{ 25}\\ \swarrow \searrow \\ \text{ 5 }\cdot \text{ 5}\end{array}$

Thus, the prime factorization of $100$ is $2\cdot 2\cdot 5\cdot 5\text{ or }{2}^2\cdot 5^2$ .