The number 9724
9724 is a composite number with 24 divisors. Its prime factorisation is × 11 × 13 × 17. Divisors (24): 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286 … 9724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9724: a Harshad number: divisible by its digit sum 22.
- 2
9724 is composite. Its prime factorisation is
- 3
The divisors add up to 21168; without 9724 itself that is 11444, so 9724 is abundant (11444 is more than 9724). Euler's totient φ(9724) = 3840 numbers up to 9724 share no factor with it.
- 4
The digits of 9724 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9724 = 2^{2} \times 11 \times 13 \times 17 \]9724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 21168 |
| Euler totient φ(n) | 3840 |
| Square | 94556176 |
| Cube | 919464255424 |
| Square root | 98.610344 (= 2√2431) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 166 |
| Scientific notation | 9.724 × |
9724 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and twenty-four |
| Binary (base 2) | 10010111111100 |
| Octal (base 8) | 22774 |
| Hexadecimal (base 16) | 25FC |
| Base 3 | 111100011 |
| As time | 9724 seconds = 2 h 42 min 4 s |
Is 9724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9724 ÷ 2 = 4862) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9724 ÷ 4 = 2431) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9724 ÷ 11 = 884) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9724 a prime number?
No. 9724 = × 11 × 13 × 17, so it is divisible by 2.
What are the factors of 9724?
1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724.
What is 9724 in binary?
10010111111100 (hexadecimal 25FC, octal 22774).
What is the square root of 9724?
About 98.6103, exactly 2√2431.
Is 9724 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 9724?
9724 is a Harshad number: divisible by its digit sum 22.