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.

Related questions
See all questions in Least Common Multiple
Impact of this question
24612 views around the world
You can reuse this answer
Creative Commons License