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.
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.