### Video Transcript

Which of these numbers is equal to a prime number that has been doubled? Circle your answer. The options are six, eight, 16 and 18.

Well, the first thing we need to look at is what is a prime number. A prime number is a number that has exactly two factors, one and themselves. We add this to the definition because if we think about the number one, well number one has one and itself as a factor. However, it’s only got one factor, so one would not be a prime number.

So next, what we want to look at is that we’re trying to find which one of our numbers is equal to a prime number that has been doubled. So therefore, we can say that our number is equal to two multiplied by a prime. So therefore, if we use inverse operations, so we divide each side of the equation by two. We can say that our number divided by two must be equal to a prime number.

And that’s because if you’ve got two multiplied by a prime and you divide it by two, it just leaves us with the prime. And then we’ve got to do the same to the other side so we have our number divided by two.

So now, to see whether our numbers are prime when they’re divided by two, we have to divide them each by two. First, well, we’ve got six. So, six over two or six divided by two is equal to three. Then we have eight, and eight divided by two is equal to four. 16 divided by two is equal to eight. And finally, 18 divided by two is equal to nine.

Okay, so we’ve now got what the value of our numbers is, when they’ve been halved. We have to see which one of them is a prime. Well if we start the right-hand side, we’ve got nine. Well, nine is not a prime number because nine can be divided by three, because three multiplied by three is equal to nine.

Eight is also not a prime number because it can be divided by two. Because we can have four multiplied by two giving us eight. And then we have four. Well, four is not a prime number because, again, we could divide it by two. And we’ve got two multiplied by two equals four. So, it’s got more than two factors. Well, we’d automatically know that four and eight would not be prime numbers because they’re even. And there is, in fact, only one even prime number, and that’s two. And that’s because two has two factors, one and two, and the only two factors are itself and one.

So now let’s move on to the final answer, which we think should be the correct answer and should be a prime number. Well, we have three, and three is a prime number because three only has two factors. That’s three and one because three multiplied by one is three. And therefore we can say that it’s definitely prime. So, in answer to the question, which of these numbers is equal to a prime number that has been doubled? The correct answer is six, and I’ve circled the first answer six.