SNT1 More Numbers Def, LCM/HCF/Prime Factorisation

More Numbers Defintions                                                                                   

Natural numbers are whole numbers equal of greater than 0.

Example:        1 ,2 ,3, 4,… 

Rational numbers: a/b where a and b are integers and b is not 0, and terminating 

Example: 2/3, 6/7, -4/5, 1.2, -10.8, 200, -430

Irrational numbers: Real numbers that cannot be written as a/b

Example: π, √2

Real numbers: The limit of convergent sequence of rational numbers; rational and irrational numbers.

Lowest Common Factor

The smallest common multiples of two or more numbers

Example

   Find the LCM of 8 and 20

                        2  | 8  20

                        2  | 4  10  

                              2   5

            LCM is 2 x 2 x 2 x 5 = 40

Highest Common Factor (for NA/O)

Largest factor that divides 2 numbers without remainder.

Example 

Find the HCF of 12 and 32 

                 2  |   12    32   (smallest common divisible no=2 for 12,32, place result below)

                 2  |     6    16   (  " " " " = 2 for  6, 16, place result below)

                           3      8   (no more common divisible number)

            HCF = 2 x 2 = 4

Example

Find the HCF of 24 and 30 (Multiplying all factors that appear in both list)

            24 = 2 x 2 x 2 x 2 x 3,          30 = 2 x 3 x 5

            HCF is 2 x 3 = 6

Prime factorisation (for NA/O)

Numbers in the form of product of prime numbers

Example:         6 = 2 x 3, 

                      18 = 2 x 3 x 3

Practice:

1.  Find all the prime numbers that are less than 70 and greater than 60. 

2. List all the prime numbers between 20 and 35