Factors

 

 

 

The factors of  a number are all the numbers which divide into it exactly.

Factors could be thought of as the atoms of the number,since factor pairs multiply together to make the number.

Every factor has a partner.

Examples

When algebra is involved,remember to look at all of the combinations.

 

Highest Common Factor (HCF)

The largest factor that two or more numbers have in common is called the HCF.

Examples

Find the HCF of 12 and 32

Find the HCF of 45 and 27

 

Find the HCF of 36x and 12x²

 

Prime Factors

Prime numbers can only be divided exactly by themselves or 1.

List of first fifteen prime numbers
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

• To work out prime factors,split the sum into a multiple of a prime number.
• Keep going until you only have prime numbers left.
• Show these numbers multiplied together.

Example

Write 88 as a product of its prime factors
 

 88 = 11 x 2 x 2 x 2
       = 11 x 2³

 

Multiples

A multiple of a number can be exactly divided by that number.

Multiples could be thought of as building blocks made by the number,since multiples are in the times table of the number.

Multiples of 5 are 5, 10, 15, 20…….
Multiples of 12 are 12, 24, 36, 48…….
Multiples of 3x² are 3x², 6x², 9x² 12x²…….

Lowest Common Multiple (LCM)

The LCM of two or more numbers is the lowest number which is a multiple of both numbers.

Example

• Find the LCM of 6 and 8

Multiples of 6 are 6, 12, 18, 24, 30, 36,42, 48, 54, 60, 66,72 ..
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72…
The LCM of 6 and 8 is 24    

• Place in order   smallest first.

   

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72….
Multiples of 20 are 20, 40, 60, 80, 100…

The LCM of 5, 8 and 20 is 40
 

 Solution : In order