Chapter 4.1, Problem 69E

To determine

To find other numbers which are factors of a number whose factor is 18.

Answer to Problem 69E

  $1,2,3,6,9,and18.$

Explanation of Solution

Given Information: Number 18 is given which is a factor of another number.

Formula used: Find the factors of 18 and they are surely the factors of another number.

Calculation:

Any number which is a factor of 18 will be a factor of the other number. Since they are the multiples of 18, they will also be multiples of the latter number.

For instance, let’s take 36. 18 is a factor of 36 and, the factors of 18 will be the factors of 36 as well.

Since the Factors of 18 are all the numbers that can evenly divide into 18, simply divide 18 by all numbers up to 18 to see which ones result in an even quotient.

  $\begin{array}{l}18÷1=18\\ 18÷2=9\\ 18÷3=6\\ 18÷6=3\\ 18÷9=2\\ 18÷18=1\end{array}$

The Positive Factors of 18 are therefore all the numbers used to divide (divisors) above to get an even number. Here is the list of all Positive Factors of 18 in numerical order:

  $1,2,3,6,9,and18.$

Now let’s find the factors of 36.

  $\begin{array}{l}36÷1=36\\ 36÷2=18\end{array}$

Continuing it further-

  $\begin{array}{l}36÷3=12\\ 36÷4=9\\ 36÷6=6\\ 36÷9=4\\ 36÷12=3\\ 36÷18=2\\ 36÷36=1\end{array}$

Here is the list of all Positive Factors of 36 in numerical order:

  $1,2,3,4,6,9,12,18,and36.$

Hence proved.