Video: Using Multiplication Equations to Identify Factors and Multiples

We know that 4 × 5 = 20. Pick the true statement. [A] 4 is a multiple of 20 [B] 5 is a multiple of 20 [C] 20 is a multiple of 5 [D] 20 is a factor of 4 [E] 20 is a factor of 5

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Video Transcript

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.

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