# Understanding Factors, Highest Common Factor, and Multiples

Learn about factors, how to find the highest common factor (HCF) between two numbers, and identifying multiples in this comprehensive guide. Explore examples and methods for determining HCF, factors of specific numbers like 40, and how to find common factors and multiples efficiently.

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## Presentation Transcript

**Starter**36 6 9 3 7 3 5 88 2 4 12 11 Using the numbers in the white box find pairs that multiply or divide together to give you totals to the below (you can only use each number once!) c) 12 d) 24 f) 20 a) 18 b) 63 e) 8**Factors**A FACTOR is a number which goes into another number without leaving a remainder i.e. from the starter you saw 2 12 = 24 As this makes 24 exactly this means that 2 and 12 are FACTORS of 24 Task: How else can you make 24 using multiplication? So the factors are 1,2,3,4,6,8,12 and 24**Factors**Write down all the factors of 40 40**Factors**Write down all the factors for the following: a) 60 b) 56 c) 102**Highest Common Factor**(HCF) We have already seen the factors of 24 and 40 as the following: 24 : 1, 2, 3, 4, 6, 8, 12 and 24 40 : 1, 2, 4, 5, 8, 10, 20 and 40 A COMMONFACTOR is a number which appears in both factors for two different numbers So for 24 and 40 the common factors are 1,2,4,8**Highest Common Factor (HCF)**The HIGHEST COMMONFACTOR is the largest number which appears in the list of common factors The common factors of 24 and 40 are 1, 2, 4 and 8 Therefore the largest number in this list is 8 So the highest common factor is 8 A method to find HCF between two numbers: 1. Write the factors for each number 2. Write the common factors which appear 3. The largest of these will be the HCF**Find the HCF**1) 12 and 20 2) 48 and 88 *3) 88 and 121**Multiples**The MULTIPLES of a number are all the numbers in the times table of that particular number For example the multiples of 2 are: 2 4 6 8 10 12 14**Multiples**2 , 6 , 12 , 21, 28 , 36 , 49 , 64 From the above numbers : 1. List the multiples of 2 2. List the multiples of 7 3. Which number is multiple of 9?**Lowest Common Multiple (LCM)**A COMMONMULTIPLE is a number that is a shared multiple of two or more numbers For example 24 is a common multiple of 8 and 12 because it appears in both the 8 and 12 times table 8 3 = 24 12 2 = 24**Lowest Common Multiple (LCM)**The LOWESTCOMMONMULTIPLE is the smallest common multiple shared by two or more numbers The multiples of 5 are : 5 , 10 , 15 , 20 , 25 , 30 , 35 , The multiples of 6 are : 6, 12 , 18 , 24 , 30 , 36 , 42 , The lowest common multiple of 5 and 6 is 30 as it is the first multiple found in both lists A method to find LCM between two numbers: 1. Write the multiples for each number 2. Circle any common multiples that appear 3. The smallest of these will be the LCM**Find the LCM**1) 4 and 6 2) 5 and 7 *3) 12 and 9**Helpful Things To Know**Factors always come in pairs i.e. 1 8 2 4 1 and the number itself are always factors 2 is always a factor of an EVEN number You can always work out if a number is a multiple of 9 by adding its digits. If the sum is 9 then it is a multiple 81 => 8 + 1 = 9 27 => 2 + 7 = 9 171 => 1 + 7 + 1 = 9 4608 => 4 + 6 + 0 + 8 = 18 ; 1 + 8 =9**Summary**The HIGHEST COMMONFACTOR is the largest number which appears in the list of common factors A method to find HCF between two numbers: 1. Write the factors for each number 2. Write the common factors which appear 3. The largest of these will be the HCF The LOWESTCOMMONMULTIPLE is the smallest common multiple shared by two or more numbers A method to find LCM between two numbers: 1. Write the multiples for each number 2. Circle any common multiples that appear 3. The smallest of these will be the LCM