What it does
Is 98,736 divisible by 9? This page runs every school divisibility rule from 2 to 11 on any whole number you type (up to 30 digits) and, more importantly, shows why the rules work:
- A row of buttons, one for each divisor from 2 to 11, each with a ✓ or ✗.
- Tap one to see the rule worked with your digits, and the real division (quotient and remainder) next to it, so you can trust the rule.
- A place value picture: for 3 and 9, each digit’s value split into a multiple of 9 and the digit itself; for 11, a multiple of 11 and ± the digit.
- Digital roots (add digits until one is left; the remainder on dividing by 9) and casting out nines, a quick check of a multiplication.
It fits Class 8 Mathematics, number play (divisibility tests, digit sums, digital roots and number puzzles). To find common factors and multiples, try the HCF and LCM; for more number properties, the number theory toolkit.
How to use it
- Type a whole number or tap an example. Commas are ignored.
- Green ✓ means it divides exactly. Tap a divisor to see its rule and the picture.
- In Digital root and remainders, type a second number to check a multiplication by casting out nines.
A worked example
The page starts with 98,736. The ones digit 6 is even (✓ 2); 36 is a multiple of 4 (✓ 4); 736 = 8 × 92 (✓ 8). The digit sum is 9 + 8 + 7 + 3 + 6 = 33, a multiple of 3 but not of 9 (✓ 3, ✗ 9), so it is also divisible by 6. From the right, 6 − 3 + 7 − 8 + 9 = 11 (✓ 11). It is not a multiple of 7 (✗). The digital root is 98736 → 33 → 6, and indeed 98,736 = 9 × 10,970 + 6.
Check yourself
Five fresh questions on remainders, digital roots and missing digits. Type a number, press Check, and open the worked answer if you need it.
FAQ
Does casting out nines prove a multiplication is right? No: it catches most mistakes, but swapping two digits, for example, keeps the digital root the same.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- The divisibility rules, digit sums, digital roots and casting out nines are standard number theory (place value and remainders). Wording, pictures and examples are fibub's own.
- Checked against Python's % operator for the example numbers and, on 3,000 random numbers of up to 30 digits, every rule's verdict against the true remainder.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-10.