- Real Numbers:- those all numbers which can be represented on the number line that is the real number.
Example: -3, -2, -1, 0, 1, 2, 3 etc.
- Rational Numbers:- A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.
Example: 23 , 52 , 21 etc.
- Natural Numbers: - Positive Integer is a natural number.
Ex. 1, 2, 3, 4, 5, ………… +infinity
- Whole Numbers:- whole numbers do not contain fraction, decimal, and negative integers.
Ex. 0,1,2,3,4,5…………..
- Prime Numbers:- Numbers that have exactly two divisors are called prime numbers.
Note**
- 1 is not a prime number
- 2 is only even prime number
- Composite numbers:- numbers that have more than two divisors are called a composite number.
Note**
4 is the smallest composite number.
- Perfect Numbers: - number for which sum of all the factors of that number must be equal to that number are called perfect numbers.
Ex. Factor of 6 = 1,2,3 and 1+2+3 = 6
It means that 6 is the Perfect Number.
- Factorial Numbers:- Product of N natural numbers called n factorial.
Ex.
We can remember these all number system by
Divisibility Rule
A Number is divisible by | Definition | Example |
2 | Last digit must be an even number | 2, 4 ,6 ,8 458, 982 |
3 | Sum of digit divisible by 3 | 123 1+2+3=6 and 6 divisible by 3 |
4 | Last two digit of the number divisible by 4 | 8724 24 divisible by 4 |
5 | Last digit either 5 or 0 | 15430, 76585 are divisible by 5 |
6 | The number divisible by both 2 and 3 | 24 It is divisible by both 2 and 3 |
7 | You can double the last digit and subtract the sum from the rest of the number and then set answer divisible by 7 then that number divisible by 7 | 672 Double last digit 2+2=4 Now subtract sum from the remaining digit then 67-4=63 And 63 divisible by 7 So, 672 divisible by 7. |
8 | Last three digit of number must be divisible by 8 | 1816 Now 816 divisible by 8. So, 1816 divisible by 8. |
9 | Sum of all the digit divisible by 9 | 153 1+5+3=9 So, 153 divisible by 9. |
10 | The number ends with 0. That must be divisible by 10. | 1000, 1980, 2000 All are divisible by 10. |
Unit Digit - The unit digit will be 2,4,6,8. it is in pair of 4.it will repeat after it.
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