The document discusses various mathematical concepts related to numbers including factors, multiples, even/odd numbers, prime/composite numbers, common factors/multiples, and divisibility rules. It provides definitions and examples for each concept. Divisibility rules are given for numbers 2 through 11 based on patterns in the digits. The document also briefly mentions highest common factor and least common multiple but does not provide details on these concepts.

1. PLAYING WITH NUMBERS

2.  FACTORS :- A number is an exact divisor of that
numbers.
For example 12 - 1,2,3,4,6,12
2,3,4,6 and 12 are factors.
 Multiples :- Multiple of a number is obtained by
multiplying it by the whole numbers.
For Example
Multiple of 2 - 2 x 1 = 2
2 x 2 = 4
2 x3 = 6

3.  Even Number :-A number which is divisible by
2 is called Even Number.
For Example – 2,4,6,8…..
 Odd Number :-A number which is not divisible
by 2 is called Odd Numbers.
For Example – 1,3,5,7…….

4.  Prime Number:-A number which have only two
factors one and number itself is called Prime
Number.
For Example – 2 - 1 x 2
3 - 1 x 3
5 – 1 x 5
 Composite Number :- A number having more than
two factor is called Composite Number .
For Example- 4 – 1x2x2
6- 1x2x3

5.  C0prime Number:-Two numbers having only one
as a common factor are called Coprime Number.
For Example – 15 and 16 are coprime number.
15- 1 x 3 x 5
16- 1 x 2 x 2 x 2 x 2
 Common Factor :-When we find the factors of two
or more numbers, and then find some factors are
the common(same) , then they are the Common
Factors.

6. For Example 6 and 8
6 – 1, 2, 3, 6
8 - 1, 2, 4, 8
 Common Multiples :-The multiples that are
common to two or more numbers are called the
common multiples of those numbers.
For Example- 2 and 3
2- 2, 4, 6, 8, 10, 12
3 – 3, 6, 9, 12, 15

7. Divisibility Rules
 Divisibility by 2:-
Unit place of the number is even then it is
divisible by 2.
Example – 24, 2582, 2480
 Divisibility by 3:-
If sum of all digit of the number is divisible by 3
the whole number is divisible by 3.
Example – 4782
4 + 7+ 8 + 2 = 21
4782 is divisible by 3

8.  Divisibility by 4:-
 If last two digit of the number is divisible by 4
the whole number is divisible by 4.
 Example - 24824
24 ÷ 4 = 6
24824 is divisible by 4
 Divisibility by 5:- If the last number is 0 or 5
then it is divisible by 5.
 Example 24680 , 24685

9.  Divisibility by 6:-
 If the number is divisible by 2 and 3 both, then it is
also divisible by6.
Example - 24822
 Divisibility by 7:-
 If the number formed after the following two steps is
divisible by 7:
 First, remove the last digit,
 Then, from the number remaining, subtract two
times the digit we just removed

10.  Example: 12,334 is divisible by 7.
 First start with the number 12,334
 Separate the last digit from the rest of the
number 1233 4
 Take two times the last digit 1233 4 × 2 = 8
 And subtract that answer from the rest of the
number 1233 – 8 = 1225
 Although it turns out that 1,225 is divisible by 7,
(1,225 ÷ 7 = 175),

11.  Divisibility by 8:- If last three digit number is
divisible by 8,then it is divisible by 8.
Example – 123216
216 ÷ 8 = 27
123216 is divisible by 8.
 Divisibility by 9:-If the sum of the numbers is
divisible by 9 then the whole numbers
divisible by 9.
Example- 2484- 2 + 4 + 8 +4 =18
2484 is divisible by 9.

12.  Divisibility by 10:- If last digit of the number is zero
then, it is divisible by 10.
Example – 12490, 248700
 Divisibility by 11:-The numbers 308, 1331 and
61809 are all divisible by 11.
 We form a table and see if the digits in these
numbers lead us to some pattern.
Example-

13. We observe that in each case the difference is either
0 or divisible by 11.All these number divisible by 11.

14. Highest Common Factor

15. Least Common Number

16. Presented BY
POOJA SINGH