Patterns
There are some special things about numbers that you can learn to recognise.
Even and Odd
- Even numbers can be divided exactly by 2. The sequence of even numbers is:
2, 4, 6, 8, 10, 12, 14 ... and so on.
Even numbers always end with a 2, 4, 6, 8 or 0. You can tell 3788, for example, is an even number because it ends with an 8. - Odd numbers cannot be divided exactly by 2. The sequence of odd numbers is:
1, 3, 5, 7, 9, 11, 13 ... and so on.
Odd numbers always end in 1, 3, 5, 7 or 9. You can tell 4399, for example, is an odd number because it ends with a 9.
Prime numbers
Prime numbers are special numbers that can only be divided by themselves and 1. This means that they only have TWO factors.
19 is a prime number. It can only be divided by 1 and 19.
The number 1 is not thought of as a prime number because it only has 1 factor.
9 is not a prime number. It can be divided by 3 as well as 1 and 9.
The prime numbers below 20 are:
2, 3, 5, 7, 11, 13, 17, 19
19 is a prime number. It can only be divided by 1 and 19.
The number 1 is not thought of as a prime number because it only has 1 factor.
9 is not a prime number. It can be divided by 3 as well as 1 and 9.
The prime numbers below 20 are:
2, 3, 5, 7, 11, 13, 17, 19
Square number
A square number is a number multiplied by itself (a number 'squared'; the symbol for squared is 2):
- 12 = 1 x 1 = 1
- 22 = 2 x 2 = 4
- 32 = 3 x 3 = 9
- 42 = 4 x 4 = 16
The square numbers up to 100 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Square Root
The square root of a number is the number you must multiply by itself to get to it. The symbol for square root is
To find the square root of 49 think, "What number multiplied by itself gives 49?" The answer is 7, because 7 x 7 = 49.
Number Sequence
A number sequence is a list of numbers that are linked by a rule.
If you work out the rule, you can work out the next numbers in the sequence. Below are some examples.
Example 19, 15, 21, 27
In this example, the difference between each number is 6:
If you work out the rule, you can work out the next numbers in the sequence. Below are some examples.
Example 19, 15, 21, 27
In this example, the difference between each number is 6:
So the rule for this sequence is to add 6 each time.
Now you can work out the next number in the sequence:
27 + 6 = 33
Example 22, 6, 18, 54
In this example, the difference between each number is different each time. You need to find a rule that fits for each number in the sequence - in this case, each number has been multiplied by 3:
Now you can work out the next number in the sequence:
27 + 6 = 33
Example 22, 6, 18, 54
In this example, the difference between each number is different each time. You need to find a rule that fits for each number in the sequence - in this case, each number has been multiplied by 3:
So the rule is to multiply by 3 each time.
Now you can work out the next number in the sequence:
54 x 3 = 162
Now you can work out the next number in the sequence:
54 x 3 = 162