The number 9
9 is a perfect square (3²) and a binary palindrome (1001). Its prime factorisation is . Divisors (3): 1, 3, 9.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9: a perfect square (3²); a binary palindrome (1001); the square of a prime (3²).
- 2
9 is composite. Its prime factorisation is
- 3
The divisors add up to 13; without 9 itself that is 4, so 9 is deficient (4 is less than 9). Euler's totient φ(9) = 6 numbers up to 9 share no factor with it.
- 4
The digits of 9 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9 = 3^{2} \]9 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 13 |
| Euler totient φ(n) | 6 |
| Square | 81 |
| Cube | 729 |
| Square root | 3 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 19 |
| Scientific notation | 9 × |
| Perfect power |
9 in other forms
| Form | Value |
|---|---|
| In words | nine |
| Roman numerals | IX |
| Binary (base 2) | 1001 |
| Octal (base 8) | 11 |
| Hexadecimal (base 16) | 9 |
| Base 3 | 100 |
| As time | 9 seconds |
Is 9 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9 ÷ 3 = 3) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9 ÷ 9 = 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9 a prime number?
No. 9 = , so it is divisible by 3.
What are the factors of 9?
1, 3, 9.
What is 9 in binary?
1001 (hexadecimal 9, octal 11).
What is the square root of 9?
3, because 3 × 3 = 9.
What is 9 in Roman numerals?
IX.
Is 9 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 9?
9 is a perfect square (3²); a binary palindrome (1001); the square of a prime (3²).