Reasoning about factors and multiples

We're told we know that 5 times 3 is equal to 15. Yep, that's true. So which of the following statements are also true? It says to choose two answers. So pause this video and see if you can work through that.

All right, now let's go through them one by one. So this first one says, "3 is a multiple of 15." Now, in order for 3 to be a multiple of 15, that means that we can multiply 15 by some whole number to get to 3. But a multiple of 15, we're thinking 15, 30, 45. It's not going to be 3. What whole number can I multiply 15 by to get 3? If I multiply 15 by 1, I'm already at 15. So this is not going to be our choice.

And since they say pick two answers, well, we might be able to figure out these, but let's just read them in to make sure that they make sense. "15 is a multiple of 3," so that means I can multiply 3 times some whole number to get to 15. And we know what that whole number is—it's 5. They tell us right over there, 5 times 3 is 15. So 15 is a multiple of 3.

15 would also be a multiple of 5 because I can multiply 5 by the whole number 3 to get to 15. So I like this choice: "5 is a factor of 15." Well, the factors of a number are numbers that you can multiply together to get that number. So 5 is a factor of 15, and 3 is a factor of 15 because 5 times 3 is 15.

So this one is also true. It would have also been true if they said "3 is a factor of 15," or if they said "15 is a multiple of 5." Any of those would have been true statements based on what we know that 5 times 3 is equal to 15.