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

1 Answer
sente
Apr 17, 2016

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.

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