A number sequence is a set of numbers arranged according to a

a certain pattern.This pattern is known as number

pattern.

EXAMPLE 1Describe the pattern of the followingnumber sequence. 4, 8, 16, 32, 64, 128, …

Solution: x2 x2 x2 x2 x2 4 8 16 32 64 128

The pattern of the sequence is to multiplythe previous number by 2.

EXAMPLE 2

Complete the following sequence. 38 880, , 1080, , 30, 5

Solution:

38 880, , 1080, , 30, 5 ÷6 ÷ 6 ÷ 6 ÷ 6 ÷ 6

The pattern is to divide the previous numberby 6.

1806480

ODD AND EVEN NUMBERS

ODD NUMBERS

EVEN NUMBERS

Whole numbers which cannot be divided

exactly by 2.Example : 1, 3, 5, 7, …

Whole numbers which can be divided exactly by 2.

Example : 2, 4, 6, 8, …

EXAMPLE 3

List all the odd numbers between 80 and 100.

Solution:

81, 83, 85, 87, 89, 91, 93, 95, 97 and 99

PRIME NUMBERS

PRIME NUMBERS

A whole number that can only be divided

exactly by itselfand the number 1

Example : 2, 3, 5, 7, 11, …

REMEMBER…1 is not a

prime number

EXAMPLE 4

List all the prime numbers that are lessthan 20.

Solution:

2, 3, 5, 7, 11, 13, 17 and 19

FACTORS

A FACTOR Can divides exactly thewhole number

REMEMBER• 1 is a factor for

all numbers• A whole number has the number itself as a factor

EXAMPLE 5

Find the factors of 14.

Solution:

14 can be divided exactly by 1, 2, 7 and 14.Factors of 14 are 1, 2, 7 and 14.

EXAMPLE 6

Determine if 8 is a factor of 103.

Solution:

103 ÷ 8 = 12 remainder 7103 cannot be divided by 8 without anyremainder.Thus, 8 is not a factor of 103.

PRIME FACTORS

PRIME FACTORS Factors of a given whole numbers which are prime

numbers

EXAMPLE 7

Find the prime factors of 12.

Solution:

Factors of 12 = 1, 2, 3, 4, 6, 12Prime factors of 12 = 2 and 3

Among the factors, 2 and 3

are prime numbers

EXAMPLE 8

Determine whether 19 is a prime factor of 418.

Solution:

418 ÷19 = 2219 is a factor of 418 and it also a prime number. Therefore, 19 is a prime factor of 418.

MULTIPLES

MULTIPLES Product of the number andanother whole number other

than zero.

EXAMPLE 9

(a) List the first five multiples of 6.

Solution:

6x1 6x2 6x3 6x4 6x5

6, 12, 18, 24, 30

(b) Determine whether 110 is a multiple of 13.

Solution:

110÷13 = 8 remainder 6Therefore, 110 is not amultiple of 13.

COMMON MUTIPLES AND LOWEST COMMON MULTIPLES (LCM)

COMMON MULTIPLES

Multiples of two or more whole numbers

Example: 6 is a multiple of 2 and 3. Therefore, the

common multiple of 2 and 3is 6.

EXAMPLE 10

(a)Find the first two common multiples of 3 and 5.(b)Determine whether 102 is a common multiple of 6 and 8.

Solution:

(a)Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … Multiples of 5 = 5, 10, 15, 20, 25, 30, … Therefore, the first two common multiples of 3 and 5 are 15 and 30.

(b) 102 ÷ 6 = 17 102 ÷ 8 = 12 remainder 6. 102 is a multiple of 6 but is not a multiple of 8. Therefore, 102 is not a common multiple of 6 and 8.

LOWEST COMMON MULTIPLES (LCM)

Smallest common multiple of two or

more numbers

There are three methods used to find

the LCM of whole numbers.

EXAMPLE 11

Find the lowest common multiple of 3, 4 and 6.Solution:

Method 1: Listing allthe multiples