Write a number as a product of its prime factors. HCF and LCM Objective Write a number as a product of its prime factors. Find the highest common factor HCF and lowest common multiple LCM of two numbers Terms and Conditions: To the best of the producer's knowledge, the presentation’s academic content is accurate but errors and omissions may be present and Brain-Cells: E.Resources Ltd cannot be held responsible for these or any lack of success experienced by individuals or groups or other parties using this material. The presentation is intended as a support material for GCSE maths and is not a comprehensive pedagogy of all the requirements of the syllabus. The copyright proprietor has licensed the presentation for the purchaser’s personal use as an educational resource and forbids copying or reproduction in part or whole or distribution to other parties or the publication of the material on the internet or other media or the use in any school or college that has not purchased the presentation without the written permission of Brain-Cells: E.Resouces Ltd.

Recap of Prime Numbers To do this work, we use prime numbers So, here is a recap of these…

Prime Numbers - A prime number is a number that can only be divided exactly (no remainder) by itself and 1 No, it can be divided by 2, 4 and 6 Is 12 a prime number? 12 ÷ 2 = 6 12 ÷ 3 = 4 12 ÷ 6 = 2 Is 7 a prime number? Yes, it can only be divided by itself and 1 7 ÷ 7 = 1 7 ÷ 1 = 7

Write down the prime numbers between 1 and 40 Notice that 1 is not a prime It’s a special number called unity 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

Factors Factors are the numbers that multiply together to make a certain number. The factor pairs of 12 are: 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 4 x 3 = 12 6 x 2 = 12 12 x 1 = 12

We can find prime factors like this… The prime factors are the prime numbers that multiply together to make a number The prime factors of 12 are 2 x 2 x 3 = 12 All prime numbers We can find prime factors like this…

How to Find Prime Factors Find any two factors of 12 12 If prime, stop 2 6 If not prime, find two more factors 3 2 Prime factors of 12 are 2, 2 and 3 Both prime so stop

If not prime, find two more factors An example of how to find the prime factors of 40 40 Find any two factors of 40 10 4 If not prime, find two more factors 2 5 Prime factors of 40 are 2, 2, 2 and 5 All prime stop

Find the prime factors of these numbers: 1. 20 2. 150 3. 60 4. 210 5. 462 6. 350 7. 390 8. 693

Find the prime factors of these numbers: 1. 20 2, 2 and 5 2. 150 2, 3, 5 and 5 3. 60 2, 2, 3 and 5 4. 210 2, 3, 5 and 7 5. 462 2, 3, 7 and 11 6. 350 2, 5, 5 and 7 7. 390 2, 3, 5 and 13 8. 693 3, 3, 7 and 11

What do we mean by the highest common factor HCF of two numbers?

Here is a method for more difficult numbers… Highest Common Factor (HCF) This is the largest number that will divide exactly (no remainder) into two numbers. The HCF of 8 and 12, for example, is 4 It’s easy to see that 4 is the largest number that will divide into both Here is a method for more difficult numbers…

36 = 2 x 2 x 3 x 3 72 = 2 x 2 x 2 x 3 x 3 2 x 2 x 3 x 3 HCF = HCF = 24 Find the highest common factor (HCF) of 36 and 72 Find the prime factors of both numbers 36 = 2 x 2 x 3 x 3 72 = 2 x 2 x 2 x 3 x 3 2 x 2 x 3 x 3 Use one of each of the numbers that are in both lists like this… HCF = HCF = 24

Find the highest common factor (HCF) of these pairs of numbers: 1. 12 and 30 2. 24 and 156 3. 54 and 180 4. 32 and 104 5. 48 and 144 6. 72 and 168 7. 45 and 75 8. 66 and 110

Find the highest common factor (HCF) of these pairs of numbers: 1. 12 and 30 6 2. 24 and 156 12 3. 54 and 180 18 4. 32 and 104 8 5. 48 and 144 48 6. 72 and 168 7. 45 and 75 15 8. 66 and 110 22

What do we mean by the lowest common multiple LCM of two numbers?

Here is a method for more difficult numbers… Lowest Common Multiple (LCM) This is the smallest number that is in the times table of both numbers. The LCM of 9 and 12, for example, is 36 Here is a method for more difficult numbers… 1 x 12 = 12 2 x 12 = 24 3 x 12 = 36 4 x 12 = 48 1 x 9 = 9 2 x 9 = 18 3 x 9 = 27 4 x 9 = 36

Find the lowest common multiple (LCM) of 24 and 60 Find the prime factors of both numbers 24 = 2 x 2 x 2 x 3 60 = 2 x 2 x 3 x 5 2 x 2 x 3 Use one of each of the numbers that are in both lists LCM = x 2 x 5 And ALL the remaining numbers LCM = 120

Find the lowest common multiple (LCM) of these pairs of numbers: 1. 18 and 30 2. 24 and 84 3. 30 and 75 4. 48 and 60 5. 18 and 24 6. 36 and 60 7. 54 and 120 8. 72 and 150

Find the lowest common multiple (LCM) of these pairs of numbers: 1. 18 and 30 90 2. 24 and 84 168 3. 30 and 75 150 4. 48 and 60 240 5. 18 and 24 360 6. 36 and 60 180 7. 54 and 120 1080 8. 72 and 150 5600