Factors, Highest Common Factors & Least Common Multiples

A factor is a number that can be divided into another number without leaving a remainder.  For example, 5 is a factor of 10 because it goes in to 10 exactly.  8 has 4 factors (1,2,4 and 8).  Whilst prime numbers like 7 or 11 always have 2 factors (1 and the number)

Write down the numbers from 1 to 30.  For each number write down the factors of that number.

Tip: Once you reach 'halfway' in a number, the only next available factor is the number itself.  E.g. the last 2 factors of 30 are 15 and 30.

Here is a game to help you revise factors...

Highest common factors
If you take 2 numbers, such as 16 and 24, you can often find factors that go into both numbers.
For example
Factors of 16: 1,2,4,8,16
Factors of 24: 1,2,4,6,12,24

In these two numbers some factors are common (the same). 1,2 & 4
4 is the highest of these factors so....

...The highest common factor of 16 and 24 is 4

Find the HCF of the examples written on the board.

Here is a game to help you revise highest common factors

Least common multiple

Another way of exploring relationships between numbers is to look for the least common multiple of those numbers.

A multiple is any number in a particular times table.
For example, 
Multiples of 5 are...5,10,15,20,25,30, 40, 45, 50 etc. 
Multiples of 4 are...4, 8, 12, 16, 20, 24, 28, 32, 36, 40 etc

You can see that 20 and 40 are common to both the 4 and 5 times tables.  Since 20 is the smaller number, it is called the 'Least Common Multiple'

Find the least common multiple (LCM) of the numbers you have been given.

Here is another fruitshoot game to revise your understanding of LCM
Or, if you prefer something different, have a snowball fight!