Write three factors of 30 that are not factors of 15.
The best way to make sure that we find all the factors of a number is to think of them in their factor pairs. Which numbers do we multiply together to give a number? To begin with, let’s find all the factor pairs that make 30: one times 30, two times 15, three times 10, and five times six. So we know that factors of 30 are one, two, three, five, six, 10, 15, and 30.
In this problem, we’re being asked to find factors of 30 that are not factors of 15. So let’s write out the factor pairs that make 15 so that we can compare them. There are a list of these. One times 15 and three times five. The factors of 15 are one, three, five, and 15.
To solve the problem, we need to look at our factors of 30 and write down three of them that are not factors of fifteen. Let’s start by crossing out the factors that are factors of 15: one, three, five, and 15. So the factors of 30 that are not factors of 15 are those that are left: two, six, 10, and 30.
There are four factors of 30 that are not factors of 15. But the problem asked us to write three factors. So we can write any three of these four numbers. We could write six, 10, and 30 or 10, two, and 30. In this video, let’s just write the first three. But what we’ll do is write a little note for ourselves that we could have chosen any three out of those four.
So although we’ve given a possible answer here, any three of the factors two, six, 10, and 30 would be a correct answer. First, we listed the factors of 30 in pairs. Then, we found the factors of 15 and we crossed out all of the factors of 30 that were factors of 15. This left us with four factors of 30 that were not factors of 15. And so, we could choose any three of these factors to answer the problem.
The three factors that we chose in this video were two, six, and 10.