What are the common multiples of 8?

Understand the Problem

The question is asking for the common multiples of the number 8. This includes identifying the multiples of 8, which are values that can be obtained by multiplying 8 by any integer.

Answer

The common multiples of 8 are: $8, 16, 24, 32, 40, 48, 56, 64, 72, 80, \ldots$

Steps to Solve

List the multiples of 8

To find the common multiples of 8, we start by multiplying 8 by integers. The first few integers are 1, 2, 3, 4, and so forth.

So, we calculate:

$8 \times 1 = 8$
$8 \times 2 = 16$
$8 \times 3 = 24$
$8 \times 4 = 32$
$8 \times 5 = 40$

This gives us the first five multiples of 8: 8, 16, 24, 32, and 40.

Identify additional multiples

Continuing with more integers, we can find additional multiples:

$8 \times 6 = 48$
$8 \times 7 = 56$
$8 \times 8 = 64$
$8 \times 9 = 72$
$8 \times 10 = 80$

Now we can compile more multiples: 48, 56, 64, 72, and 80.

Compile the list of common multiples

Now we combine our findings into a single list of common multiples of 8.

The common multiples so far include:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Summarize the common multiples

The common multiples of 8 can be expressed generally as $8n$, where $n$ is any integer (1, 2, 3, ...).

This means that for any integer value substituted for $n$, you can find a multiple of 8.

The common multiples of 8 include: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, and so on.

More Information

The common multiples of a number are essential in many areas of mathematics, particularly in understanding relationships between integers and ratios. Every multiple of 8 can be represented as $8n$, where $n$ is any integer.

Tips

Mixing up multiples with factors: Remember that multiples are the products of a number with integers, while factors are numbers that divide another number without leaving a remainder.
Forgetting to include larger integers can lead to an incomplete list of common multiples.

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