# Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 12

GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 12

03:11

### Video Transcript

The grid shows five numbers. 22, 23, 24, 25, 26. From the numbers in the grid, part one: state the prime number. Part two: state the square number.

Right, to answer part one of this question, we need to remember the definition of a prime number. A prime number is a number which has exactly two factors. Now, you may have had the definition that a prime number is a number which can only be divided by one and itself. But there’s a problem with this definition, if we consider the number one.

Now, one fits the second description of a prime number because it can be divided by one and also it can be divided by itself, as itself is one. However, one is not a prime number. So if instead, we use this first definition, that a prime number is a number which has exactly two factors, we can see that one is not a prime number as it does not have two distinct factors. So we’ll use the definition of a prime number as a number which has exactly two factors rather than a number which can be divided by one and itself.

To find the prime number in the list, we need to look for the number then which only has two factors. Each number will have themselves and one as two factors. So we’re looking to see whether they have any others. We can eliminate all of the even numbers straightaway, as they can all be divided by two. Now two, in fact, is the only even prime number. All other even numbers are not prime. So we’re left with just 23 and 25.

Now 25, you’ll probably recognize from your five times table. It’s equal to five multiplied by five. Which means 25 is not a prime number as it has three factors: one, five, and 25. 23 is the only number left and it is indeed a prime number. You could check this by seeing if you can divide it by numbers like three. And you’ll always find that there is a remainder. In any case, it’s a good idea to try and be familiar with prime numbers up to about 30 so that you can recognize them easily.

Now, let’s consider part two of the question where we’re asked to state which number is a square number. A square number is the result of multiplying a positive integer or whole number by itself, which is called squaring a number. For example, nine is a square number because it’s equal to three multiplied by three. We can list out some square numbers to help us answer this question.

One multiplied by one is one. Two multiplied by two is four. Three multiplied by three is nine, as we’ve already said. Four multiplied by four is 16. And five multiplied by five, which we also saw in part one of this question, is 25. 25 is the only one of these numbers that appears in the grid. So 25 is the square number. It’s also a good idea to memorize square numbers up to about 12 squares, as you could be asked about square numbers in lots of different contexts.