MTH/P/5: NUMBER PATTERNS AND SEQUENCES

Types of numbers.

1)       Whole numbers       0, 1, 2, 3, 4, 5, ………….

2)       Counting numbers/ Natural numbers                1, 2, 3, 4, 5, ………….

3)       Odd numbers: These are numbers that give a remainder when divided by 2

{1, 3, 5, 7, ……………….}

4)       Even numbers: These are ones that are exactly disable by two

{0, 2, 4, 6, 8, 10, ……………….}

5)       Prime numbers: These are numbers with only two factors.

{2, 3, 5, 7, 11, 13, ……………….}

6)       Composition numbers: These are numbers with more than 2 factors

{4, 6, 8, 9, 10, 12, ……………….}

7)       Square numbers: These are numbers got by multiplying a number by its self.

{1, 4, 9, 16, 25, ……………….}

8)       Cubic numbers: These are got by multiplying the same number three times.

{1, 8, 27, 64, ……………….}

9)       Triangular numbers: These are got by adding consecutive counting numbers.

{1, 3, 6, 10, 15, 21, ……………….}

⁺2 ⁺3 ⁺4 ⁺5   ⁺6

MULTIPLES AND L.C.M

Take note of the limits

*Less than

*From to

*between ……………. And ………..

*The first………………..

Examples

40. i) List down the multiples of 6 between 20 and 40.

{24, 30, 36}

12. ii) List down the first 5 multiples of 12.

M₁₂ = {12, 24, 36, 48, 60}

Finding lowest common multiple by listing down multiples

Example

DIVISIBILITY TESTS

These show which number is exactly divisible by another given number.

Divisibility test for 2.

A number is divisible by 2 if the last digit is an even number

i,e 0, 2, 4, 6, 8, …………..

Divisibility test for 3.

A number is divisible by 3 if the sum of its digits is divisible by 3.

Example.

State whether 144 is divisible by 3.

Sum of the digits              1 + 4 + 4

= 9

9 is divisible by 3

144 is divisible by 3.

Divisibility test for 4

A number is divisible by 4 if its last two digits are zero or divisible by 4.

Divisibility test for 5

A number is divisible by 5 if its last digit is either 0 or 5.

Divisibility test for 10

A number is divisible by 10 if its last digit is 0.