# Important formulas from Number System for CAT/XAT/IIFT/NMAT/SNAP/MICAT/CMAT

**1.Natural number :** Counting numbers 1,2,3,4 etc are called natural numbers.

**2.Whole Numbers :** Natural Numbers and 0

**3.Integers :** All natural numbers, 0, and negative numbers together form the set of integers.

{…….-3, -2, -1, 0, 1, 2, 3….}

**4.Even number : **The number divisible by 2 eg 2,4,6

**5.Odd number :** The number not divisible by 2 eg. 1,3,5

**6.Prime number :** A number greater than 1 and has exactly two factors 1 and itself

To find whether a number is Prime or not, we find Prime no. less than its square root and check whether no is divisible by any of those Prime no if yes it is not Prime else its a Prime no.

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There are 25 prime numbers between 1 and 100 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.)

**7.Co-primes :** Two numbers a and b are said to be co-primes, if their H.C.F. is 1

**Divisibility Rules**

**Divisible by 2 –** if it’s unit digit is any of 0,2,4,6,8

**Divisibility by 3 –**if the sum of digits is divisible by 3

**Divisible by 4 –** if its last two digit is divisible by 4

**Divisible by 5 – ** if it’s unit digit is either 0 or 5.

**Divisible by 6 –** if it is divisible by 2 and 3.

**Divisible by 8-** if it’s last 3 digit is divisible by 8.

**Divisible by 9-** if the sum of digit is divisible by 9.

**Divisible by 10-** if its unit digit is 0.

**Divisible by 11 –** if the difference of the sum of it’s digits at odd places and the sum of it’s digits at even places is either 0 or a number divisible by 11.

**Divisibility By 12- ** if it is divisible by both 4 and 3.

**Divisibility By 14** – if it is divisible by 2 as well as 7.

**Divisibility By 15 —** if it is divisible by both 3 and 5.

**Divisibility By 16 —**if the number formed by the last 4 digits is divisible by 16.

**Points to remember**

- If a number is divisible by p as well as q, where p and q are co-primes, then the given number is divisible by pq. If p arid q are not co-primes, then the given number need not be divisible by pq, even when it is divisible by both p and q.
- Dividend=Divisor*quotient + Remainder
- HCF*LCM=Product of numbers
- 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
- (1
^{2}+ 2^{2}+ 3^{2}+ ….. + n^{2}) = n ( n + 1 ) (2n + 1) / 6 - (1
^{3}+ 2^{3}+ 3^{3}+ ….. + n^{3}) = (n(n + 1)/ 2)^{2} - Sum of first n odd numbers = n
^{2} - Sum of first n even numbers = n (n + 1)

Important formula

- (a + b)(a – b) = (a
^{2}– b^{2}) - (a + b)
^{2}= (a^{2}+ b^{2}+ 2ab) - (a – b)
^{2}= (a^{2}+ b^{2}– 2ab) - (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2(ab + bc + ca) - (a
^{3}+ b^{3}) = (a + b)(a^{2}– ab + b^{2}) - (a
^{3}– b^{3}) = (a – b)(a^{2}+ ab + b^{2}) - (a
^{3}+ b^{3}+ c^{3}– 3abc) = (a + b + c)(a^{2}+ b^{2}+ c^{2}– ab – bc – ac) - When a + b + c = 0, then a
^{3}+ b^{3}+ c^{3}= 3abc - (a + b)
^{n}= a^{n}+ (^{n}C_{1})a^{n-1}b + (^{n}C_{2})a^{n-2}b^{2}+ … + (^{n}C_{n-1})ab^{n-1}+ b^{n}

You must remember all the concepts mentioned above, Do add if I missed anything in comment section..

All the Best !!

Nice collection of formulas…. Thank you