Finding the Greatest Three-Digit Multiple of 8

The question asks for the greatest three-digit number that is a multiple of 8. A three-digit number is any whole number from 100 to 999.

A multiple of 8 is a number that can be divided by 8 without leaving a remainder.

To find the greatest three-digit number that is a multiple of 8, we can start with the largest three-digit number, which is 999, and see if it is divisible by 8. If not, we can find the largest multiple of 8 that is less than 999.

Step-by-Step Calculation

Let's divide 999 by 8:

\begin{equation*} \frac{999}{8} \end{equation*}

We can perform long division or calculate it as follows:

\begin{align*} 999 &= 8 \times 100 + 199 \\ 199 &= 8 \times 20 + 39 \\ 39 &= 8 \times 4 + 7 \end{align*}

So, $999 = 8 \times 100 + 8 \times 20 + 8 \times 4 + 7$.

This means $999 = 8 \times (100 + 20 + 4) + 7$, which simplifies to $999 = 8 \times 124 + 7$.

Alternatively, using long division:

When 999 is divided by 8, the quotient is 124 and the remainder is 7. This means 999 is not a multiple of 8.

To find the largest multiple of 8 less than 999, we subtract the remainder from 999:

$999 - 7 = 992$

Let's verify if 992 is a multiple of 8:

$992 \div 8 = 124$.

Since the remainder is 0, 992 is a multiple of 8.

Also, 992 is a three-digit number.

Since we started with the largest three-digit number (999) and found the largest multiple of 8 less than or equal to it, 992 must be the greatest three-digit number that is a multiple of 8.

Checking the Options

Let's quickly look at the given options:

• 984: $984 \div 8 = 123$. This is a multiple of 8, but it is smaller than 992.
• 992: $992 \div 8 = 124$. This is a multiple of 8.
• 998: $998 \div 8$ leaves a remainder (as calculated before). Not a multiple.
• 989: $989 \div 8$ leaves a remainder. Not a multiple.

Comparing the multiples of 8 from the options, 992 is the largest.

Therefore, the greatest three-digit number which is a multiple of 8 is 992.