Aptitude- Number System

Types of number:


1. Natural Numbers: 1,2,3,… so on
2. Whole numbers: 0,1,2,3… so on
3. Integers: it can be negative or positive numbers. Negative numbers are -2, -1 and Positive numbers are 1,2,3..so on and ‘0’ is non-positive and non-negative number.
4. Prime numbers: the number which is divisible by itself or 1. Eg, 2,3,5..so on. ‘2’ is the smallest prime number.
5. Perfect Number: If the sum of the divisors of a number N excluding N itself is equal to N, then N is called perfect number. For example:
6= 1+2+3 (divisors of 6)= 6 -> hence it is perfect number
28= 1+2+4+7+14=28
6.  Composite number: numbers other than prime number. Eg, 4, 6, 8, 10.. so on
7.  Co-prime numbers; the combination of numbers whose HCF is 1. Eg, (2,3), (4,5), (7,9) etc
Note: ‘1’ is neither prime nor composite number.
 -Important Formulae:

1.  The sum of n natural numbers= n(n+1)/2
2.  The sum of even natural numbers= n(n+1)
3.  The sum of odd natural numbers= n2
4.  The sum of square of n natural numbers= n(n+1)(2n+1)/6
5.  The sum of cube of n natural numbers= [n(n+1)/2]2

-Important Points to remember:

1.  The smallest 1 digit prime number is 2
2. The smallest 2 digit prime number is 11
3. The smallest 3 digit prime number is 101
4. The smallest 4 digit prime number is 1009
5. The largest 1 digit prime number is 7
6. The largest 1 digit prime number is 97
7. The largest 1 digit prime number is 997
8. The largest 1 digit prime number is 9973