Number reference
9 explained.
9: nine, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- nine
- Classification
- composite
- Factors
- 1, 3, 9
- Prime factorization
- 3 × 3
- Square root
- 3
- Cube root
- 2.080084
- Binary
- 1001
- Octal
- 11
- Hexadecimal
- 9
- Roman numeral
- IX
- Digit sum
- 9
- Digital root
- 9
What makes 9 notable
- Perfect square. 9 = 3², so a square of side 3 has an area of 9.
9 in everyday use
Nine innings make a baseball game and nine players take the field for each side. It is the atomic number of fluorine, the count of justices on the United States Supreme Court, and the nominal length of a human pregnancy in months. Cats are said to have nine lives, the Greek Muses numbered nine, and the nine-to-five workday gave a name to office routine. A cat-o'-nine-tails, a nine-dart finish, and cloud nine all draw on the sense that nine is the last stop before ten.
Nine is three squared and the largest single digit in base ten, which gives it a famous trick: the digits of any multiple of 9 add up to a multiple of 9, so 9 × 7 = 63 and 6 + 3 = 9. Bookkeepers used this as "casting out nines" to check arithmetic. Nine is also 1 + 8, the sum of the first two cubes, and the smallest odd composite number.
Nearby numbers
How to read this page
The factor list shows every way 9 splits into equal whole-number groups — 3 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 9 for contexts that do not use decimal.
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