## Introduction

### Definition

- A factor is a number that divides another number without a remainder.
**Number****Factors**1 2

1 ,2,3,4,6,1 2

1 6

1 ,2,4,8,1 6

39

1 ,3,1 3,39

A natural number with only two factors, one and itself is a prime number. Or any number that only can be divided by 1 and itself. Prime numbers have exactly 2 different factors

## Prime Numbers up to 100.

2 | 3 | 5 | 7 | 11 |

13 | 17 | 19 | 23 | 29 |

31 | 37 | 41 | 43 | 47 |

53 | 59 | 61 | 67 | 71 |

73 | 79 | 83 | 89 | 97 |

## Composite Numbers

- Any number that has more factors than just itself and 1 .They can be said to be natural number other than 1 which are not prime numbers.They can be expressed as a product of two or more prime factors.

9 = 3 x 3

12 = 2 x 2 x 3

105 = 3 x 5 x 7 - The same number can be repeated several times in some situations.

32 = 2 x 2 x 2 x 2 x 2 = 2^{5}

72 =2 x 2 x 2 x 3 x 3 = 2^{3}x 3^{2} - To express a number in terms of prime factors ,it is best to take the numbers from the smallest and divide by each of them as many times as possible before going to the next.
**Example**Express the following numbers in terms of their prime factors- 300
- 196

Solution-
2

300

2

150

3

75

5

25

5

5

1

300 = 2 x 2 x 3 x 5 x 5

= 2^{2}x 3 x 5^{2} -
2

196

2

98

7

49

7

7

1

= 2^{2}x 7^{2}

## Exceptions

- The numbers 1 and 0 are neither prime nor composite.
- 1 cannot be prime or composite because it only has one factor, itself.
- 0 is neither a prime nor a composite number because it has infinite factors.
- All other numbers, whether prime or composite, have a set number of factors. 0 does not follow the rules.

## Past KCSE Questions on the Topic

- Express the numbers 1470 and 7056, each as a product of its prime factors.

Hence evaluate:

1470^{2}

√(7056)

Leaving the answer in prime factor form - All prime numbers less than ten are arranged in descending order to form a number
- Write down the number formed
- What is the total value of the second digit?

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