Sun, 19 Sep
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# Numbers

Numeral: In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.
A group of digits, denoting a number is called a numeral.
of 1 of 2 3 E.g. 123 1 2 3 100 20 3

## Types of Numbers

Natural Counting numbers 1, 2, 3, 4, … 0, 1, 2, 3, … [all counting numbers with zero] Positive: {1, 2, 3, 4, …}; Negative Integers: {-1, -2, -3, …}; Non-Positive & Non-Negative Integers: 0 2, 4, 6, 8, … [A number divisible by 2] 1, 3, 5, 7, … [A number not divisible by 2] [>1 & has exactly two factors, namely 1 and the number itself]. Up to 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, 97} #25 prime numbers. Greater 100: 191 is not divisible by 2, 3, 5, 7, 11, 13 4, 6, 8, 9, … [>1 & not prime] (2,3), (4,5), (7,9), (8,11), etc. [H.C.F is 1]

## Divisibility Rules

By Condition Example
2 Unit digit will be any of 0, 2, 4, 6 or 8. 2402
3 Sum of all digits divisible by 3. 312. 3 + 1 + 2 = 6.
4 Last 2 digits divisible by 4. 2316
5 Unit digit is either 0 or 5. 505
6 Divisible by both 2 and 3. 18
8 Last 3 digits divisible by 8. 1288
9 Sum of all digits divisible by 9. 504. 5 + 0 + 4 = 9.
10 Unit digit should be 0. 5340
11 Difference of sum of odd place digits & even place digits is either 0 or divisible by 11. 6402. [(2 + 4) - (0 + 6)] = 0

## Number Series

 1 (1+2+3+...+n) = n(n+1)/2 2 (12+22+32+...+n2) = [n(n+1)(2n+1)]/6 3 (13+23+33+...+n3) = [n2(n+1)2]/4