Topics include square and cube numbers, types of numbers, prime and composite numbers and more...... like it if you feel it good :)

2. TYPES OF
NUMBERS
Topic # 1 in Mathematics

3. 1) NATURAL NUMBERS
Natural
Numbers are 1,2,3,4,
5 but zero is not
a Natural Number.

4. 2) WHOLE NUMBERS
Whole
Numbers are 1,2,3,4,
5 plus zero.

5. 3) EVEN NUMBERS
Even Numbers are
that can be divided
into two equal groups
like 0,2,4,6,8.

6. 4) ODD NUMBERS
Odd Numbers are
that cannot be
divided into two equal
groups like 1,3,5,7,9.

7. 5) ORDINAL NUMBERS
Ordinal Numbers are
that defines the position
of something in a series
like 1st,2nd,3rd.

8. 6) CARDINAL NUMBER
Cardinal
Numbers tell us the
quantity of something
in present
like 1,2,3,4,5,6,7,8,9.

9. 7) DECIMAL NUMBERS
"Decimal number" is often used
to mean a number that uses a
decimal point followed by digits
that show a value smaller than one.
Example: 45.6 (forty-five point six)
is a decimal number.

10. FACTORS AND
MULTIPLES
Topic # 2 in Mathematics

11. 2) FACTORS
Factors are what we
can multiply to get
the number.

12. FACTS ABOUT FACTORS
1) Factors of a number are written in ascending order.
2) The lowest factor of every number is 1.
3) The highest factor of every number is the number itself.
4) The factors of any numbers are finite.
5) The factor of a number is its complete divisor i.e.
remainder is 0. For example, as we know 6 is the factor of
12 the answer is 2 and there is no remainder.

13. 1) MULTIPLES
Multiples are what
we get after
multiplying the
number by an integer.

14. FACTS ABOUT MULTIPLES
1) If you need to know the multiples of any number you need
to remember the table of that number.
2) The lowest multiple of any number is the number itself.
3) The highest multiple of any number is infinity.
4) The multiples of 2 are even numbers.

15. PRIME AND COMPOSITE
NUMBERS
Topic # 3 in Mathematics

16. 1) PRIME NUMBERS
A prime number (or a
prime) is a natural
number greater than 1
that is not a product of
two smaller natural
numbers.

17. 2) COMPOSITE NUMBERS
Composite Numbers
are the numbers which
have more than two
factors.

19. DIVISIBILITY RULES
Topic # 4 in Mathematics

20. DIVISIBILITY RULE : -
There are some rules which
help us to find that a
number (no matter how
big) is divisible by the given
divisor without doing any
calculation.

21. DIVISIBILITY RULE OF 1
Each and every number is
divisible by 1 because 1 is the
factor of every
number.

22. DIVISIBILITY RULE OF 2
A whole number whose last
digit is Even is divisible by 2.
45 678
4 539 246
3 957

23. DIVISIBILITY RULE OF 3
Add the digits of the number,
if the sum is multiple of 3
then the whole number is
divisible by 3.
44 = 4 + 4 = 8
45 = 4 + 5 = 9

24. DIVISIBILITY RULE OF 4
If the last two digits of a
number are 00 or form a
number which is divided by 4
then the whole
number is divisible by 4.
48 247
48 200

25. DIVISIBILITY RULE OF 5
If the last digit is 0 or 5,then
the whole number is divisible
by 5.
200
23 465
389 671

26. DIVISIBILITY RULE OF 6
If the number is divisible by 2
and 3 both then it means that
it is divisible by 6 as well.
23 908
6 342

27. DIVISIBILITY RULE OF 7
Double the ones place i.e.
multiply by 2 . Subtract it from
the rest of the number . If the
answer is multiple of 7 , then
the whole number is divisible
by 7.
693

28. DIVISIBILITY RULE OF 8
If the last three digits of a
number are 000 or form a
number which is divided by 8
then the whole number is
divisible by 8.
3 294 732
3 294 000

29. DIVISIBILITY RULE OF 9
Add the digits of the number, if
the sum is multiple of 9 then the
whole number is divisible by 9.
65 241 = 6+5+2+4+1 =18
9 854 = 9+8+5+4 = 26

30. DIVISIBILITY RULE OF 10
The last digit of the number
should be 0.
257 890
25 789

31. PRIME FACTORIZATION
Topic # 5 in Mathematics

32. PRIME FACTORIZATION
Prime factorization is
a method to find the prime
factors of a given number
 Division Method
 Tree Method

33. 1) TREE METHOD
Suppose, we have to find the prime factors of
16.
1. We consider the number 16 as the root of the
tree.
2. We write a pair of factors as the branches of
the tree i.e., 2 × 8 = 16
3. We further factorize the composite factor 8 as
4 and 2, and again the composite factors 4 as 2
and 2.
We repeat the process again till we get the prime
factors .

34. 2) DIVISION METHOD
I: First we divide the number by the smallest
prime number which divides the number exactly.
II: We divide the quotient again by the smallest
or the next smallest prime number if it is not
exactly divisible by the smallest prime number.
We repeat the process again and again till the
quotient becomes 1. Remember, we use only
prime numbers to divide.
III: We multiply all the prime factors.
Remember, the product is the number itself.

35. INDEX NOTATION
Topic # 6 in Mathematics

36. INDEX NOTATION
Index Notation is a shortcut
for writing repeated
multiplication by the same
number.

37. Simple Index Notation
64
35
62
6 x 6 x 6 x 6
3 x 3 x 3 x 3 x 3
6 x 6

38. PERFECT SQUARES
AND
PERFECT CUBES
Topic # 7 in Mathematics

39. PERFECT SQUARES
Perfect Squares is a
product of 2 equal
integers.

40. PERFECT CUBES
Perfect Cubes is a
product of 3 equal
integers.

41. Squares Cubes
1 × 1 = 1
2 × 2 = 4
3 × 3 = 12
4 × 4 = 16
5 × 5 = 25
6 × 6 = 36
7 × 7 = 49
8 × 8 = 64
9 × 9 = 81
10 × 10 = 100
1 × 1 x 1 = 1
2 × 2 x 2 = 8
3 × 3 x 3 = 27
4 × 4 x 4 = 64
5 × 5 x 5 = 125
6 × 6 x 6 = 216
7 × 7 x 7 = 343
8 × 8 x 8 = 512
9 × 9 x 9 = 729
10 × 10 x 10 = 1000

42. HOW TO FIND SQUARE OF
DIFFERENT NUMBERS USING
PRIME FACTORIZATION :-
a) 84 2 84
2 42
3 21
7 7
1
84 2 x 2 x 3 x 7
2 x 3 x 7 42 Ans

43. For Example your answer is 42 so you
have to simply do it multiply from 2
and if the answer is the same as
question so it means it is correct.

44. HOW TO FIND CUBE OF
DIFFERENT NUMBERS USING
PRIME FACTORIZATION :-
a) 1000 2 1000
2 500
2 250
5 125
5 25
5
1000 2x2x2x5x5x5
2 x 5 10 Ans

45. For Example your answer is 10 so you
have to simply do it multiply from
and if the answer is the same as
question so it means it is correct.