| E.g. 123 | of 1 | of 2 | 3 |
|---|---|---|---|
| Face Value | 1 | 2 | 3 |
| Place Value | 100 | 20 | 3 |
| Natural | Counting numbers 1, 2, 3, 4, … |
|---|---|
| Whole | 0, 1, 2, 3, … [all counting numbers with zero] |
| Integers | Positive: {1, 2, 3, 4, …}; Negative Integers: {-1, -2, -3, …}; Non-Positive & Non-Negative Integers: 0 |
| Even | 2, 4, 6, 8, … [A number divisible by 2] |
| Odd | 1, 3, 5, 7, … [A number not divisible by 2] |
| Prime |
[>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 |
| Composite | 4, 6, 8, 9, … [>1 & not prime] |
| Co-prime | (2,3), (4,5), (7,9), (8,11), etc. [H.C.F is 1] |
| 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 |
| 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 |
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