This question aims to find an expression that has both the given factors. Moreover, it is helpful to have a number divisible by the given numbers.

This question is based on the concepts of **arithmetic**, and the factors of a number include all divisors of that specific number. The **factors** of the number 16, for example, are 1, 2, 4, and 16. We can obtain another whole integer number by dividing 16 with any of the numbers given above.

## Expert Answer

We are looking for an expression that has 8 and $ n $ as factors. Therefore, suppose that $ E $ is the expression that has a factor, which means that the expression is divisible by 8.

Hence,

\[ E (X) = 8 X . ( n )^X \]

Where $ X $ is any positive integer $ n $.

\[ E (X) = 8 X ( n )^X \]

### Alternate Solution

From the question, we have $ 8 $ and $ n $ as factors of an expression. Moreover, these factors should be present in the expression. The example is as follows:

\[ x = 8 + n \]

## Numerical Results

The expression that has both 8 and n as factors is as follows.

\[ E (X) = 8 X ( n )^X \]

or an alternate solution could be:

\[ x = 8 + n \]

## Example

We have a number 8 with exactly four different factors, including 1, 2, 4, and 8. Therefore, if you have a number 36, how many factors does it have?

**Solution**

**Step 1:**Total number of factors number 36 can be calculated as follows:

\[ 36 = 2 \times 2 \times 3 \times 3 \]

\[ 36 = 2^2 \times 3^2 \]

\[ (36) = ( 2 + 1 ) \times ( 2 + 1 )\]

\[ = 3 \times 3 \]

\[ = 9 \]

So the number 36 has exactly 9 factors.

**Step 2:** The number of factors of the number 36 are as follows:

$ 1 \times 36 = 36 $

$ 2 \times 18 = 36 $

$ 3 \times 12 = 36 $

$ 4 \times 9 = 36 $

$ 6 \times 6 = 36 $

$ 9 \times 4 = 36 $

$ 12 \times 3 = 36 $

$ 18 \times 2 = 36 $

$ 36 \times 1 = 36 $

With this, the factors of **36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36**.

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