# Factors

We need to understand prime numbers and factors before we can find the prime factors of a number.

# Prime Numbers

A prime number can only be divided by itself and 1. A prime number does not have any remainders. The table below shows prime numbers up to 60

Prime Numbers | ||||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 5 | 7 | 9 | 11 |

17 | 19 | 23 | 29 | 31 | 37 | 39 |

41 | 43 | 47 | 51 | 53 | 57 | 59 |

# Factors

Factors are whole numbers that can be multiplied together to equal a product.

Example 1

2 × 8 = 16

2 and 8 are factors and

16 is the product.

Example 2

3 × 5 = 15

3 and 5 are factors and

15 is the product.

# Factors of a Number

Now we are going to find the factors of a number.

Factors of 4

1 × 4 = 4

2 × 2 = 4

Factors of 4 are: 1,2 and 4

Factors of 6

1 × 6 = 6

2 × 3 = 6

Factors of 6 are: 1,2,3 and 6

Factors of 8

1 × 8 = 8

2 × 4 = 8

Factors of 8 are: 1,2,4 and 8

Factors of 9

1 × 9 = 9

3 × 3 = 9

Factors of 9 are: 1,3 and 9

# Prime Factors of a Number

We know what** prime numbers** and **factors** are, so now we are going to find the **prime factors** of a number using two different methods.

Example 1: Prime Factors of 18

Method 1

- Divide 18/2 = 9

9 is not a prime number

so we continue dividing - Divide 9/3 = 3

3 is the final prime number - The prime factors of 18:

**2 x 3 x 3 = 18**

Method 2

This is the tree method.

Use the tree method for finding the prime factors for large numbers.

Example 2: Prime Factors of 24

- Divide 24/2 = 12

12 is not a prime number

so we continue dividing - Divide 12/2 = 6

6 is not a prime number

so we continue dividing - Divide 6/2 = 3

3 is the final prime number - The prime factors of 24:

**2 x 2 x 2 x 3 = 24**

This is the tree method.

# Lowest Common Multiple (LCM)

To find the LCM of 6 and 8 we need to know the mutiples of 6 and 8 (times table for 6 and 8).

Multiples of 6

6, 12, 18, 24, 30, 36, 42,48

Multiples of 8

8, 16, 24, 32, 40, 48, 56

We can see the numbers 24 and 48 appear in both the multiples. The smallest number is 24 so the LCM is 24.

Tree Method (LCM)

We can also use the tree method to find the LCM of two numbers.

Finding the LCM of 6 and 8 using the tree method:

**Step 1: ** Find the prime factors of 6 and 8.

Prime Factors of 6

Prime Factors of 8

**Step 2: ** Now we have to find the tree with the most 2s and 3s.

Prime factors of **6** are 2 x 3

Prime factors of **8** are 2 x 2 x 2

- The tree with the most 2s is tree 8.

It has: 2 x 2 x 2 - The only tree with a 3 is tree 6.

It has: 1 x 3 - Multiply the numbers: 2 x 2 x 2 x 3 = 24

LCM = 24

# Highest Common Factor (HCF)

To find the HCF of 24 and 36 we need to know the factors of 24 and 36.

Factors of 24

1 x 24

2 x 12

3 x 8

4 x 6

**Factors of 24:**

1,2,3,4,6,8,12,24

Factors of 36

1 x 36

2 x 18

3 x 12

4 x 9

6 x 6

**Factors of 36:**

1,2 ,3,4,6,9,12,18,36

The numbers common in both of the lists are: 1,2,3,4,6 and 12. The hightest common factor is 12.

HCF= 12

Tree Method

We can also use the tree method to find the HCF of 24 and 36.

**Step 1:** Find the prime factors

Prime Factors of 24

Prime Factors of 36

**Step 2: ** Look for the common factors.

The common factors of 24 and 36 are coloured in green.

2 | x | 2 | x | 2 | x | 3 | = | 24 |

2 | x | 2 | x | 3 | x | 3 | = | 36 |

**Step 3: **Mutlply the common factors from one of the list to find the HCF.

**2 x 2 x 3 = 12**

HCF= 12