Question

What's a multiple of 4? What does that mean?

Answer 1

A multiple of `4` is any number which can be written in the form `4n` where `n` is an integer.

Explanation:

In general, given two values `a` and `b`, we say that `b` is a multiple of `a` if `b=na` for some integer `n`.

For example, `-4, 0, 4, 12,` and `100` are all multiples of `4` because

`-4 = 4xx-1`
`0 = 4 xx 0`
`4 = 4xx1`
`12 = 4xx3`
`100 = 4xx25`

On the other hand, values such as `1` or `10` are not multiples of `4`, as

`1 = 4xx1/4`
`10 = 4xx5/2`

`1/4` and `5/2` are not integers.

It is generally correct to state that `b` is a multiple of `a` if `b/a` is an integer, although this requires `a!=0`.

Intuitively, it makes sense to call these values multiples, as they are the values which can be obtained by adding or subtracting your original value multiple times. A multiple of `4` is a number which can be written as
`4+4+4+...+4`
or
`4-4-4-...-4`.
Note that this is equivalent to the above definitions.