## Types of Numbers

### A prime number has only two factors, itself and 1.

e.g {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43...}

23 is a prime number because it has only two factors, 1 and itself, 23.

### Fermat Numbers

These are numbers of the form + 1 where n is a positive integer:

when n = 0 this gives the first Fermat number 21 + 1 = 3

when n = 1 this gives the second Fermat number 22 + 1 = 5

when n = 2 this gives the third Fermat number 24 + 1 = 17

when n = 3 this gives the fourth Fermat number 28 + 1 = 257 and so on...

### Fibonacci Numbers

These numbers belong to the sequence { 1, 1, 2, 3, 5, 8, 13, 21...} where each number is the sum of the two numbers before it.

1st term = 1
2nd term = 1
3rd term = 1+ 1 = 2
4th term = 1 + 2 = 3 and so on...

### Perfect Numbers

A perfect number is a counting number which equals the SUM of all its factors except itself.

e.g. 6 is a perfect number. Factors are {1, 2, 3, 6} Sum of factors (except 6) = 6

28 is a perfect number. Factors are {1, 2, 4, 7, 14, 28} Sum of factors (except 28) = 28

### Triangle number

A triangle number is the number that can be shown as a pattern of dots in the shape of a triangle.

i.e. {1, 3, 6, 10, 15, 21, 28, 36, 45...}

First triangle number is 1 Second triangle number is 3 Third triangle number is 6 Fourth triangle number is 10 ### Composite Number

A composite number is a number with more than two factors. i.e. The non-prime numbers

i.e. 4, 6, 8, 9, 10, 12, 14...

### Platonic Solids

There are only FIVE polyhedra which have every face the same regular polygon.

These are:

• tetrahedron (4 faces-each a triangle)
• cube (6 faces-each a square)
• octahedron (8 faces-each a triangle)
• dodecahedron (12 faces-each a pentagon)
• icosahedron (20 faces each a triangle)

### Palindrome

A number (or word) which reads the same backwards e.g. 34543, 44, 1000001

### Factorial (n!)

The factorial of a positive integer n is the product of all the positive integers up to and including n . For example: 6! = 5 x 4 x 3 x 2 x 1 = 720 