Number System

Updated on 17/02/26 by Mananjay MahatoShare on WhatsApp
Number Square () Cube ()
2 4 8
3 9 27
4 16 64
5 25 125
6 36 216
7 49 343
8 64 512
9 81 729
10 100 1000
11 121 1331
12 144 1728
13 169 2197
14 196 2744
15 225 3375
16 256 4096
17 289 4913
18 324 5832
19 361 6859
20 400 8000
21 441 9261
22 484 10648
23 529 12167
24 576 13824
25 625 15625
26 676 17576
27 729 19683
28 784 21952
29 841 24389
30 900 27000
31 961 29791
32 1024 32768
33 1089 35937
34 1156 39304
35 1225 42875
36 1296 46656
37 1369 50653
38 1444 54872
39 1521 59319
40 1600 64000
41 1681 68921
42 1764 74088
43 1849 79507
44 1936 85184
45 2025 91125
46 2116 97336
47 2209 103823
48 2304 110592
49 2401 117649
50 2500 125000

 

multiplication tables from 12 to 25

12 13 14 15 16 17 18
24 26 28 30 32 34 36
36 39 42 45 48 51 54
48 52 56 60 64 68 72
60 65 70 75 80 85 90
72 78 84 90 96 102 108
84 91 98 105 112 119 126
96 104 112 120 128 136 144
108 117 126 135 144 153 162
120 130 140 150 160 170 180
19 20 21 22 23 24 25
38 40 42 44 46 48 50
57 60 63 66 69 72 75
76 80 84 88 92 96 100
95 100 105 110 115 120 125
114 120 126 132 138 144 150
133 140 147 154 161 168 175
152 160 168 176 184 192 200
171 180 189 198 207 216 225
190 200 210 220 230 240 250

factorial

  • n!=n×(n−1)×(n−2)×…×3×2×1
  • 0! = 1
  • 1! = 1
  • 4!=4×3×2×1=24
  • 5!=5×4×3×2×1=120
  • 6!=6×5×4×3×2×1=720

Numbers

  • Natural Numbers (N): Counting numbers (1, 2, 3…).
  • Whole Numbers (W): Natural numbers plus zero (0, 1, 2, 3…).
  • Integers (Z): Whole numbers and their negatives (…, -2, -1, 0, 1, 2...).
  • Rational Numbers (Q): Can be written as a fraction (p/q). Includes integers and terminating/repeating decimals (e.g., 1/2, 0.75, -3).
  • Irrational Numbers: Cannot be written as a fraction. Non-repeating, non-terminating decimals (e.g., Π,√2).
  • Real Numbers (R): All numbers on the number line (Rationals + Irrationals).
  • Imaginary Numbers: Square roots of negative numbers (e.g., 2i, where i = √-1).
  • Complex Numbers (C): Combination of real and imaginary (a + bi).
  • Prime: Only two factors (1 and itself). Ex: 2, 3, 5.
  • Composite: More than two factors. Ex: 4, 6, 8.
  • Even: Divisible by 2. Ex: 2, 4, 6.
  • Odd: Not divisible by 2. Ex: 1, 3, 5.
  • Co-prime numbers:  pairs with a Highest Common Factor (HCF) of 1 (e.g., 8 and 15)
  • Twin primes :  pairs of prime numbers that differ by exactly 2 (e.g., 3 and 5).

Divisibility Rule

  • 2 Rule: Last digit is even (0,2,4,6,8).
    Ex: 128 → Last digit 8 (Even) → Yes
  • 4 Rule: Last two digits divisible by 4.
    Ex: 1124 → Last two digits 24 (24÷4=6) → Yes
  • 8 Rule: Last three digits divisible by 8.
    Ex: 3120 → Last three digits 120 (120÷8=15) → Yes
  • 3 Rule: Sum of digits is divisible by 3.
    Ex: 123 → 1+2+3 = 6 (6÷3=2) → Yes
  • 9 Rule: Sum of digits divisible by 9.
    Ex: 729 → 7+2+9 = 18 (18÷9=2) → Yes
  • 5 Rule: Last digit is 0 or 5.
    • Ex: 225 → Last digit 5 → Yes
  • 10 Rule: Last digit is 0.
    Ex: 250 → Last digit 0 → Yes
  • 25 Rule: Last two digits are 00, 25, 50, or 75.
    Ex: 1375 → Last two digits 75 → Yes
  • 6 Rule: Divisible by both 2 and 3.
    Ex: 144 → Even (2) and 1+4+4=9 (3) → Yes
  • 7 Rule: Double last digit, subtract from rest, result divisible by 7.
    Ex: 203 → 20 – (2×3=6) = 14 (14÷7=2) → Yes
  • 11 Rule: Difference between sum of digits at odd and even places is 0 or multiple of 11.
    Ex: 121 → (1+1) – 2 = 0 → Yes
  • 12 Rule: Divisible by both 3 and 4.
    Ex: 144 → Sum 1+4+4=9 (3) and last two digits 44 (4) → Yes
  • 13 Rule: Multiply last digit by 4, add to rest, repeat, result divisible by 13.
    Ex: 169 → 16 + (9×4=36) = 52 → 5 + (2×4=8) = 13 (13÷13=1) → Yes
  • 14 Rule: Divisible by both 2 and 7.
    Ex: 112 → Even (2) and 11 – (2×2=4) = 7 (7) → Yes
  • 15 Rule: Divisible by both 3 and 5.
    Ex: 225 → Sum 2+2+5=9 (3) and last digit 5 (5) → Yes
  • 16 Rule: Last four digits divisible by 16.
    Ex: 1136 → Last four digits 1136 (1136÷16=71) → Yes
  • 17 Rule: Multiply last digit by 5, subtract from rest, result divisible by 17.
    Ex: 289 → 28 – (9×5=45) = -17 (17) → Yes
  • 18 Rule: Divisible by both 2 and 9.
    Ex: 324 → Even (2) and 3+2+4=9 (9) → Yes
  • 19 Rule: Multiply last digit by 2, add to rest, repeat, result divisible by 19.
    Ex: 209 → 20 + (9×2=18) = 38 → 3 + (8×2=16) = 19 → Yes
  • 20 Rule: Last two digits divisible by 20 (00,20,40,60,80).
    Ex: 340 → Last two digits 40 (20×2) → Yes
  • 21 Rule: Divisible by both 3 and 7.
    Ex: 441 → Sum 4+4+1=9 (3) and 44 – (1×2=2) = 42 (7) → Yes
  • 22 Rule: Divisible by both 2 and 11.
    Ex: 242 → Even (2) and (2+2) – 4 = 0 (11) → Yes
  • 23 Rule: Multiply last digit by 7, add to rest, repeat, result divisible by 23.
    Ex: 529 → 52 + (9×7=63) = 115 → 11 + (5×7=35) = 46 (46÷23=2) → Yes
  • 24 Rule: Divisible by both 3 and 8.
    Ex: 1248 → Sum 1+2+4+8=15 (3) and last three digits 248 (8) → Yes
Number System