Multiples and Factors
A common factor is a factor that is shared by two or more numbers.
To find the highest common factor (HCF):
- list the factors of the two numbers
- select the highest factor on both lists.
A common multiple is a number that is a multiple of two or more numbers.
To find the lowest common multiple (LCM) of two numbers:
- list multiples of the higher number until you get to one that is divisible by the smaller number.
Example 1
What is the highest common FactorA factor of a particular number is a number that divides into it evenly or exactly, leaving no remainders
Solution
- List the factors of the two numbers
- The factors of 12 are 1, 2, 3, 4, 6, 12
- The factors of 18 are 1, 2, 3, 6, 9, 18
- Select the highest factor on both lists.
- The highest number which is on both lists is 6.
Answer
The HCF is 6.
Example 2
What is the lowest common multiple of 5 and 8?
Solution
- List multiples of the higher number until you get to one that is divisible by the smaller number
- 8, 16, 24, 32, 40,
- 40 is the first multiple of 8 that is divisible by 5.
Answer
The LCM is 40.
Question
15 is the highest common factor of 30 and another number. The other number is between 40 and 50.
What is the other number?
Solution:
15 is a factor of 15, 30, 45, 60, 鈥
45 is the only number between 40 and 50 so the other number is 45.
Question
Pens are sold in packs of 12 and notebooks in packs of 10. Suzi wants to buy the same number of pens and notebooks.
What is the least number she can buy?
Solution:
The least number she can buy will be the lowest common multiple.
List the multiples of 12 until finding one that is divisible by 10.
Hint! It must end with a zero.
12, 24, 36, 48, 60
60 is the first multiple of 12 which is also divisible by 10.
Answer
The least number she can buy is 60.
Test yourself
More on M2: Number
Find out more by working through a topic
- count5 of 6
- count6 of 6
- count1 of 6