What you need to know

Things to remember:

  • 2 is special, it is the only even prime number.
  • 5 is the only prime number that ends in a 5.
  • Other than 2 and 5 by themselves, all prime numbers end with a 1, 3, 7, or 9.

So, what is a prime number? A prime number is a number bigger that 1 that can’t be divided by anything other than itself and 1. We can also think of this as it only has two factors, 1 and itself!

Is 15 a prime number?

Factors of 15: 1, 3, 5 and 15.

15 has more than two factors, so is not prime.

You need to be able to remember the prime numbers less than 20:

2                      3                      5                      7

11                    13                    17                    19

If we look at our table of numbers up to 100, you’ll notice that some of them are coloured in red; these are our prime numbers.

 

 

We can look at this table to learn some important points that will help us to identify prime numbers.

If we look at the even numbers (they end with a 2, 4, 6, 8, or 0) we can learn three important points:

  • Only 2 is coloured in, so it must be our only even prime.
  • All even numbers have 2 as a factor, so have AT LEAST three factors.
  • If you’re asked if any even number is other than 2 is prime, you can immediately say no!

If we look at the numbers ending with a 5, we can learn two important points:

  • 5 is the only prime number than ends with a 5.
  • All numbers that end in a 5 have 5 as a factor, so have AT LEAST three factors.

If we look at the numbers that end with a 1, 3, 7, or 9, we can learn one important point:

  • Prime numbers that aren’t 2 or 5 always end with a 1, 3, 7, or a 9.

Let’s look at some numbers and use these points to decide if they are prime or not.

18 – Is not prime, it is even.

15 – Is not prime, it ends in a 5.

37 – Ends in a 7, it COULD be prime (This one actually is prime).

33 – Ends in a 3, it COULD be prime (This one is not prime, 3 is a factor).

Example Questions

Question 1: Is 25 a prime number?

Answer

25 is not a prime number, we can divide it by 5.

Question 2: Is 67 a prime number?

Answer

67 ends with a 7, so it could be prime… And it is true, 67 is a prime number!