We know that four times five equals
20. Pick a true statement. a) Four is a
multiple of 20. b) Five is a multiple of 20. c) 20 is a multiple of five. d) 20 is a
factor of four. And e) 20 is a factor of five.
It seems like we need to know the
definition of the word multiple and of the word factor. Factors and multiples are different
things. They both involve
multiplication. Factors are what we multiply
together to get a number. A multiple is the result of
multiplying a number by an integer.
But consider this, four as a
multiple of 20. If four is a multiple of 20, four
has to equal 20 times an integer. And an integer is a whole
number. It’s not a fraction. There’s not a whole number we could
multiply 20 by to equal four. And for that same reason, five
can’t be a multiple of 20. There’s no integer. There’s no whole number that you
multiply 20 by that would equal five.
The next statement says 20 is a
multiple of five. 20 is five times some integer. Is there a whole number that we
multiply five by that will equal 20? Yes, five times four equals 20. Four is an integer. And that makes 20 a multiple of
five. c works.
Let’s go ahead and consider our
last two options. d says 20 is a factor of four. Again, if 20 is a factor of four,
then you can multiply 20 by some integer and get four. Saying 20 is a factor of four is
the same thing as saying four is a multiple of 20. And it’s not true. Saying 20 is a factor of five is
the same thing as saying five is a multiple of 20. And it’s false.
The only true statement here is
that 20 is a multiple of five.