13 × 13 = 169.

# Properties of Numbers (Difficult)

Some numbers are prime numbers - some numbers have other properties. In this Maths quiz, you will get some more practice in dealing with the properties of numbers. See how well you can do to improve your 11-plus grades.

As you continue through school and maths lessons, you'll learn a lot more about numbers. For now, we are dealing with the easy stuff, so make sure you get 10 out of 10 in both this quiz and our other one on properties of numbers.

If you choose to go further with maths when you leave school, no doubt you will come across some strange terms for numbers. Most likely, you've heard of infinity ~ this means without end ~ and numbers go on forever. Saying this, you will learn about Graham's number, TREE(3) and a googolplex!

Getting back to this quiz, we're counting on you getting a good score!

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1. Which number is the odd man out: 49, 15, 41, 9?
They are all odd, but 41 is also a prime number: a prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1
2. For those of you with stamina: How many prime numbers are there between 1 and 100 inclusive?
Well done those of you who bothered to do this question. The rest of you - do it later. There are 25 prime numbers between 1 and 100. Here they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Phew! Does anyone want to find out how many prime numbers there are between 1 and 1,000 inclusive? Just joking! Here's the answer anyway: 168 prime numbers. I wonder if your teacher knows that? By the way, prime numbers are a big thing in higher maths
3. Which of the following statements is wrong?
7 + 5 = 12 which is not odd. If you want to show that a statement is not always true, find one example that shows it is wrong - like we did here
4. What is the smallest prime number?
A prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1, e.g. 2, 3, 17, 41
5. Which number is the odd man out: 71, 17, 11, 39?
They are all odd numbers, but only 39 is a non prime number: a prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1
6. How many prime numbers are there between 1 and 30?
Here they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
7. Which number is the odd man out: 64, 32, 144, 100?
They are all even numbers, but 32 is not a square number. A square number (perfect square) is a number formed by the multiplication of another number with itself, e.g. 144 = 12 × 12; 64 = 8 × 8; 100 = 10 × 10. Note: 1 × 1 = 1
8. Which of the following statements is wrong?
11 + 7 = 18 which is not a prime number. If you want to show that a statement is not always true, find one example that shows it is wrong - like we did here
9. Which of the following statements is wrong?
13 × 13 = 169! D'oh! By the way, just because 13 is odd, this doesn't prevent it from being a prime number too
10. Which two prime numbers have to be added together to give 38?
This is the only choice that has two prime numbers

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