Table of Contents
Types of Number
Digits: – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits. There are 10 digits.
Number- A number is denoted by a group of digits, known as numbers.
For example – 23, 10, 50 99, 101, 1000, 1524, 98415662
In a number all digits have a value is called place value
Place Value Table
| Ten-Crore | Crores | Ten-Lacs | Lacs | Ten-Thousands | Thousands | Hundreds | Tens | Units |
Examples- 8547312
| Ten-Crore | Crores | Ten-Lacs | Lacs | Ten-Thousands | Thousands | Hundreds | Tens | Units |
| 8 | 5 | 4 | 7 | 3 | 1 | 2 |
Eighty-Five Lacs Forty-Seven Thousand Three Hundred Twelve (8547312)
Face Value – Face value of any digit is a value of itself as per their place in a number
Example- 24563
Face value of 3 = 3 (3 is an unit place)
Face value of 6 = 6 × 10 = 60 (6 is a ten place)
Face value of 5 = 5 × 100 = 500 (5 is a hundred place)
Face value of 4 = 4 × 1000 = 4000 (4 is a thousand place)
Face value of 2 = 2 × 10000 = 20000 (2 is a ten thousand place)
Various Types of Numbers:
Natural Number: Counting numbers are called natural numbers. 1, 2, 3, 4, 5, . . . are natural numbers.
Whole Number: Counting numbers with 0 (zero) are called whole numbers. 0, 1, 2, 3, 4, 5, . . . are whole numbers.
Integers: All counting numbers, zero and negatives of counting numbers are form set of integers.
Example . . . -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, . . . are all integers.
Even: Numbers: Natural numbers divisible by 2 is called even numbers. Ex 2, 4, 6, 8, 10, . . .
Odd Numbers: Natural numbers not divisible by 2 is called odd numbers. Ex 1, 3, 5, 7 , . . . are odd numbers.
Prime Numbers: If a counting number has exactly two factors, 1 and itself then it is called prime number.
Ex 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . . are prime numbers.
2=1×2, 3=1×3
6=2×3, 2 and 3 are factors of 6, but 6 is the multiple of 2 and 3
Note: 2 is an only even prime number.
Co-Prime Numbers: If two natural number ‘a’ and ‘b’ are said to be co-prime if HCF (a, b) = 1.
Ex: HCF (2, 3) = 1, HCF(4, 5) = 1 ……..
4=2×2, 6=2×3 4and 6 are not co-prime
Composite Numbers: All the counting numbers greater than 1 are not prime is called composite numbers.
Ex 4, 6, 8, 9, 10, 12, 14, …..
Rational Numbers:
- Rational numbers are those numbers which can be expressed as a ratio between two integers that is in the form of , where .
example, the fractions and −11/8 are both rational numbers.
- All the integers are included in the rational numbers, due to any integer can be written as the ratio .
2, 2/1 =2
- All decimals which terminate are rational numbers since 3.27 can be written as 327/100
- Decimals which have a repeating pattern after some points are also rational. Ex. 0.0833333…. = 1/12.
0.33333333…. =1/3 , 2.3434343434…
- The set of rational numbers is closed under all four basic operations, that is, given any two rational numbers, their sum, difference, product, and quotient is also a rational number.
8-2=6, 55+2=57, 1.02+0.22=1.24
Irrational number:
- An irrational number is a number that cannot be written as a ratio (or fraction) that is cannot be written in the form of .
- In decimal form, it never terminates or repeats pattern.
Ex. √2 = 1.41421356237309… irrational no
π=3.14159265358979….
e=2.71828182845904…
52.484769214895133251565324653………….
These all numbers are real no.
Rational +Irrational = Real No.
Click here to know video concept of Types of Numbers
Divisibility Rule of Number
First and Last digit of any numbers:
Ex: 2458976, Here 2 is the First Digit and 6 is the Last Digit.
Last digit is also known as unit place digit.
24658795247851
Divisibility Rule
Divisibility by 2: A number is divisible by 2 if unit place digit is any of, 0, 2, 4, 6, 8
Ex: 2, 10, 52, 157820, 578964166222
Divisibility by 3: If the sum of all digits of a number is divisible by 3, then the number is also divisible by 3
Ex: 4323, 4+3+2+3 = 12, 12 is divisible by 3 so number 4323 is divisible by 3.
2547896, 2+5+4+7+8+9+6= 41 it is not divisible by 3
Divisibility by 4: If the last two digit of the number is divisible by 4 then the number is divisible by 4.
Ex: 37524, Last two digit is 24 since 24 is divisible by 4 hence 37524 is also divisible by 4.
If the last two digits will be zero then also number is divisible by 4
Ex: 2458700 this is divisible by 4
Divisibility by 5: If the last digit of the any number is 0 or 5 then number is divisible by 5.
Ex. 521789440, 54899565125, ….
Divisibility by 6: If any number is divisible by 2 and 3 both then the number is divisible by 6.
Ex: 5334
Last digit is 4 so it is divisible by 2.
Sum of digits is 15 and it is divisible by 3
5+3+3+4=15
So, the given number is divisible by both 2 and 3 hence 53334 is divisible by 6
Divisibility by 7: If double of unit’s place digits of given number is subtracted from rest of digits and if the remainder is divisible by 7, then that number is divisible by 7.
Or any no. written by same digit in 6 time as
444444, 777777, 222222, 555555, 888888, etc
Ex: 875
87-(2×5) = 87-10 =77
77 7 =11
Hence 875 is divisible by 7.
- This divisibility rule applicable for numbers greater than 99.
Divisibility by 8: If the Last three digits of a numbers is divisible by 8 or are 000, then the number is divisible by 8.
Ex: 96432, 432 is divisible by 8 so 96432 is divisible by 8.
84575000
Divisibility by 9: if sum of all digits of any number is completely divisible by 9 then the number is divisible by 9.
Ex: 317349
3+1+7+3+4+9 =27. 27 is divisible by 9, so, the given number is divisible by 9.
Divisibility by 10: If the last digit (unit’ place) will be zero then the number is divisible by 10.
Ex: 524960 it is divisible by 10 because its unit’ place digit is 0
Divisibility by 11: If the difference between the sum of digits at even place and sum of digits at odd place is 0 or divisible by 11. Then the number is divisible by 11.
Or if the difference between the sum of Alternat digits will 0 or divisible by 11, then the number is divisible by 11.
Ex: 7238
Here Alternat digits are 7, 3 and 2, 8
7+3 = 10 and 2+8 =10
10-10=0 hence number is divisible by 11.
Ex: 10615
1 0 6 1 5
Even place digits 0, 1 so, 0+1=1
Odd place digits 1, 6, 5 so, 1+6+5=12
12-1=11 it is divisible by 11, hence given number 10615 is divisible by 11.
Divisibility by 12: If any number is divisible by 3 and 4 then the number is divisible by 12.
Ex 34632 is divisible by 3 and 4 both so it is divisible by 12.
Divisibility by 13: If 4 times the units digit of the number plus the number obtained by removing the units digits of the number is a multiple of 13
Ex: Is 50661 divisible by 13?
Step-I: 5066 + (1×4) = 5070
Step-II: 507+(0×4) =507
Step-III: 50+(7×4) =78
So, 78 is divisible by 13, hence 50661 is divisible by 13.
Divisibility by 14: If any number is divisible by 2 and 7, then the number is divisible by 14.
Ex 448 it divisible by 2 and 7 so, it is divisible by 14.
Divisibility by 15: If any number is divisible by 3 and 5, then the number is divisible by 15.
Ex 2070 is divisible by 3 and 5 so, it is divisible by 15.
