Write each number in its correct place on the diagram: 16, 17, 18, and 19.
The diagram that we’re given is a type of Venn diagram. Remember that a Venn diagram is made up of circles or ellipses that overlap. We can think of them as like sorting circles. For example, we sort all our even numbers into the centre shape. All the prime numbers belong in the shape on the left. And any number that’s a square number belongs in the shape on the right. What about the two areas where our shapes overlap?
Any number in this area is both even and prime. There aren’t many of those. In fact, there’s only one number that is even and prime. What sort of numbers do we put in this section? Any number in this section is in the even hoop, so it must be even. But it’s also in the square number hoop, so it’s even and square.
Now that we thought about how the diagram works, let’s think about where to put each number. Which of our four numbers are prime numbers? Remember that a prime number is a number that has only two factors: one and itself. A useful way to identify prime numbers is to try to draw an array. If the only array we can make is a long line, then the number must be prime because the only factors are one and itself.
The factors of 16 are one, two, four, eight, and 16. So 16 is not a prime number. The only factors of 17 are one and 17. The only array we could make using the number 17 is a one-by-17 line. We know that 17 is prime, but where do we write the number? 17 belongs in this section because it’s a prime number, but it’s odd, not even. Let’s tick the number 17 to remind ourselves that we’ve already placed it.
Is the number 18 a prime number? The factors of 18 are one, two, three, six, nine, and 18. It has more than two factors. So it’s not a prime number. Is the number 19 a prime number? Yes, the only factors of 19 are one and itself. And again, 19 is not an even number. So we need to write it in the section of our diagram that shows prime numbers but not prime numbers that are even. Let’s tick the number 19 to show that we’ve now included this in our diagram.
We’re now left with two numbers to place: 16 and 18. We know that both numbers are even. So we know that they both belong in the central even number section of our diagram. As we’ve already noticed, neither number is prime. So this only leaves us with two possible places to write these numbers. Are they even or are they even and square?
Remember that a square number is made by multiplying another number by itself. Any number that makes an array that is square is a square number. We know that we can make a four-by-four square out of the number 16 because four times four equals 16. So 16 is both square and even. So we can write it in this overlapping section.
There are no numbers that multiply by themselves to give the number 18. So 18 is not a square number, but it is even. So we can write it in this centre section. So we used our knowledge of each type of number to work out where to write the numbers 16, 17, 18, and 19.
The number 16 is both even and square. The number 17 is a prime number and is odd. The number 18 is simply even. It’s neither prime nor square as well. And as well as the number 17, the number 19 is also a prime number that’s not even. It’s an odd, prime number. So these are the correct places where each number belongs on our Venn diagram.