The number 9729
9729 is a composite number with 12 divisors. Its prime factorisation is × 23 × 47. Divisors (12): 1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9729 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9729 is composite. Its prime factorisation is
- 3
The divisors add up to 14976; without 9729 itself that is 5247, so 9729 is deficient (5247 is less than 9729). Euler's totient φ(9729) = 6072 numbers up to 9729 share no factor with it.
- 4
The digits of 9729 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9729 = 3^{2} \times 23 \times 47 \]9729 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 14976 |
| Euler totient φ(n) | 6072 |
| Square | 94653441 |
| Cube | 920883327489 |
| Square root | 98.635693 (= 3√1081) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 166 |
| Scientific notation | 9.729 × |
9729 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and twenty-nine |
| Binary (base 2) | 10011000000001 |
| Octal (base 8) | 23001 |
| Hexadecimal (base 16) | 2601 |
| Base 3 | 111100100 |
| As time | 9729 seconds = 2 h 42 min 9 s |
Is 9729 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 (9729 ÷ 3 = 3243) | 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 6) | 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 (9729 ÷ 9 = 1081) | 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 5) | 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 9729 a prime number?
No. 9729 = × 23 × 47, so it is divisible by 3.
What are the factors of 9729?
1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729.
What is 9729 in binary?
10011000000001 (hexadecimal 2601, octal 23001).
What is the square root of 9729?
About 98.6357, exactly 3√1081.
Is 9729 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9729?
It is a composite number with 12 divisors.