This web application allows you to teach kids how to check a number can be divided by another number (primarily, but not limited to, 2, 3, 4, 5, 8, 9, 10 or 11). When they learn that, you can increase the complexity by setting a composite divisor: like 6 which is 2×3. Or by setting multiple prime or composite divisors: like 3 or 5 or 22. The latter though will be automatically converted to 2×11 for better clarity.

The application neither collects private information, nor uses cookies, and doesn't even make external calls. It just uses the browser's local storage to keep your preferences. Please note: this means that clearing your browser cache will discard the application's preferences too. Unfortunately, this will happen even if you install it as an app on your device.

The application is available on any device: tablet (ideal), phone, laptop, or desktop. The recommended orientation for the handheld devices is landscape (horizontal). The only requirements are a web browser and an internet connection to start using or to get updates.

You can use Divisiki in a browser as is without any installation. However, you can install it on most devices via browser. This will give you the native app experience and the ability to run offline when the internet connection is intermittent or unavailable. Please note that not all browsers are capable of web app installation. On handheld devices, ideally, do that with Google Chrome or Microsoft Edge on non-Apple devices, and with Safari on Apple devices. You should find and tap Add to Home screen menu item (or similar), then follow the prompts. On laptops and desktops, an icon with a monitor and an arrow might show up at the end of the address bar. If you hover it with the mouse cursor, a tooltip will pop: Install Divisiki. Click that icon and follow the prompts.

On the first start, you'll be asked to change the default player name from Anonymous to something more suitable. You can do that by tapping/clicking the modify icon (the second from the left above the list of players), then typing in any other text of your choice.

To start playing, tap/click the large play button in the center, and you'll see a random number. If it is divisible by the one(s) listed at the right bottom corner past By:, tap/click the green tick button. Otherwise, tap/click the red cross button. If your mental calculation is right, you'll get another number, and the score at the right top corner will change. Otherwise, you'll see the large play button again, but the score will stay until you start another game. You'll also see the text explaining why the game was stopped. The text will be located at the top middle part of the screen. If the game is timed, every time you give an answer, the timer at the left bottom corner will be reset. The score at the top right corner is in the format of Player C:CurScore B:BestScore L:Level. Both player and points are tappable/clickable allowing to add, change or delete player(s), or the level (the current number of digits in the riddle).

After a certain number of consecutive successful attempts, the level (the number of digits) will increase automatically For the lower levels, this will happen after the application can't find more numbers to play, and for the higher levels, after 50 successful attempts in a row. However, you can change that manually too by tapping/clicking the score at the top right corner of the screen.

You can add, rename or delete player(s) by tapping/clicking the name of the current player at the top right corner of the screen, then using the icons on top of the list of existing players in the popup dialog. The icons are (in the order of appearance): add, rename, delete, move up, move down. Please note that once a player is deleted, all their game information is lost. By deleting all players one by one, you delete all your preferences. Anonymous (default) player with the default preferences will be automatically reinstated afterwards.

You can change the level (the number of digits in the number being checked) by tapping/clicking the score at the top right corner of the screen (next to the current player name), then navigating through or tapping/clicking an item in the list of levels from 1 to 15 the respective number and closing the dialog or pressing Enter.

You can select the time limit type between Per move (default) and Per game. The differences are:

• The former will reset the countdown to the selected time limit after every successful guess
• The latter will continue the countdown after every successful guess until the time is over, then will reset

You can select various time limits by tapping/clicking the the current time limit at the left bottom corner of the screen, then navigating through or tapping/clicking an item in the list of time limits and closing the dialog or pressing Enter.

You can add, rename or delete games (divisors) for the current player by tapping/clicking the score of the current player at the bottom right corner of the screen where By: is located, then using the icons on top of the list of existing divisors in the popup dialog. The icons are (in the order of appearance): add, rename, delete, move up move down. Essentially, you add or modify divisors. For the new set of divisors, the level will be set to minimal, and the initial score will be zero. Divisors can appear either as plain prime numbers like 2 or as composite numbers like 12 or 3x4 ("and" operation) or as an "or"-separated list of numbers like 5 or 12o13 meaning that the number being played should be divisible by at least one of those numbers ("or" operation). Once you enter divisors, they'll be automatically converted to the canonical form like 5 or 4×3 or 13. Please note that composite numbers can be entered either like plain numbers or a product of simpler numbers using *, x, X or × or "a" or "and" as the operator. In any case, the result will be calculated and converted into a product of powers of prime numbers or 10. The order is ascending for the base numbers rather than powers: 4 or 3, as 4 is 2². The list of divisors ("at least one of") can be specified using the "o" or "or" with or without surrounding spaces as the separator. Please note that once you modify a game (divisors), your level and highest score will be reset.

• 2 – the lowest digit should be even (0, 2, 4, 6 or 8):
  • 20, 32, 154, 3276, 39158
• 3 – the sum of all digits is divisible by 3:
  • 12, 126, 459
• 4 – the lowest two digits make the number that is divisible by 4:
  • 24, 356
• 5 – the lowest digit is either 0 or 5:
  • 10, 135, 2480, 76905
• 7 – multiply the lowest digit by 2 and subtract the result from the remaining digits; the final result should also be divisible by 7:
  • 14 => 4 × 2 - 1 = 7
  • 357 => 35 - 7 × 2 = 21
• 8 – the lowest three digits form a number that is divisible by 8:
  • 128, 9008, 25064
• 9 – the sum of all digits should be divisible by 9:
  • 18, 927, 4671
• 10 – should end with 0:
  • 10, 120, 45700
• 11 – the sum of the even digits should be equal to the sum of the odd digits or the difference between these sums should be divisible by 11:
  • 11 => 1 = 1
  • 121 => 2 = 2
  • 5335 => 8 = 8
  • 9020 => 11 - 0 = 11
• 13 – multiply the lowest digit by 4 and add the result to the number formed by the remaining digits; the final result should be divisible by 13:
  • 13 => 3 × 4 + 1 = 13
  • 52 => 2 × 4 + 5 = 13
• 17 – multiply the lowest digit by 5 and subtract the result from the number formed by the remaining digits; the final result should be divisible by 17:
  • 17 => 7 × 5 - 1 = 34 => 4 × 5 - 3 = 17
  • 153 => 3 × 5 - 15 = 0
• 19 – multiply the lowest digit by 2 and add the result to the number formed by the remaining digits; the final result should be divisible by 19:
  • 19 => 9 × 2 + 1 = 19
  • 114 => 4 × 2 + 11 = 19
• 23 – multiply the lowest digit by 7 and add the result to the number formed by the remaining digits; the final result should be divisible by 23:
  • 23 => 3 × 7 + 2 = 23
  • 115 => 5 × 7 + 11 = 46 = 23 × 2
• 25 – the last two digits should be divisible by 25 (i.e. ending with 00, 25, 50 or 75):
  • 125, 375, 4000, 70075
• 27 – break the number into 3-digit numbers (from the lowest digit to the highest one); the sum of those numbers should be divisible by 27:
  • 85293 => 85 + 293 = 377 = 27 × 14
  • 225990 => 225 + 990 = 1215 => 1 + 215 = 216 = 27 × 8
• 29 – multiply the lowest digit by 3 and add the result to the number formed by the remaining digits; the final result should be divisible by 29:
  • 29 => 9 × 3 + 2 = 29
  • 435 => 5 × 3 + 43 = 58 = 29 × 2
• 31 – multiply the lowest digit by 3 and subtract the result from the number formed by the remaining digits; the final result should be divisible by 31:
  • 31 => 3 - 1 × 3 = 0
  • 713 => 71 - 3 × 3 = 62 = 31 × 2
• 37 – break the number into 3-digit numbers (from the lowest digit to the highest one); the sum of those numbers should be divisible by 37:
  • 89947 => 89 + 947 = 1036 = 37 × 28
  • 159914 => 159 + 914 = 1073 = 37 × 29
• 41 – multiply the lowest digit by 4 and subtract the result from the number formed by the remaining digits; the final result should be divisible by 41:
  • 41 => 4 - 1 × 4 = 0
  • 943 => 94 - 3 × 4 = 82 = 41 × 2
• 50 – the last two digits should be divisible by 50 (i.e. ending with 00 or 50):
  • 550, 2200, 30050
• 59 – multiply the lowest digit by 6 and add the result to the number formed by the remaining digits; the final result should be divisible by 59:
  • 59 => 9 × 6 + 5 = 59
  • 1357 => 7 × 6 + 135 = 177 = 59 × 3
• 79 – multiply the lowest digit by 8 and add the result to the number formed by the remaining digits; the final result should be divisible by 79:
  • 79 => 9 × 8 + 7 = 79
  • 2923 => 3 × 8 + 292 = 316 = 79 × 4
• 99 – break the number into 2-digit numbers (from the lowest digit to the highest one); the sum of those numbers should be divisible by 99:
  • 2277 => 77 + 22 = 99
  • 32175 => 75 + 21 + 3 = 99
• 101 – break the number into 2-digit numbers (from the lowest digit to the highest one); the sum of those numbers with the alternating sign should be divisible by 101:
  • 590547 => 59 - 05 + 47 = 101
  • 14900025 => 14 - 90 + 00 - 25 = -101
• 1091 – multiply the lowest digit by 109 and subtract the result from the number formed by the remaining digits; the final result should be divisible by 1091:
  • 1091 => 109 - 1 × 109 = 0
  • 4722939 => 472293 - 9 × 109 = 471312 => 47131 - 2 × 109 = 46913 => 4691 - 3 × 109 = 4364 => 436 - 4 × 109 = 0

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