The number 9744
9744 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 29. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48 … 9744.
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How to work it out
- 1
What is special about 9744: a Harshad number: divisible by its digit sum 24.
- 2
9744 is composite. Its prime factorisation is
- 3
The divisors add up to 29760; without 9744 itself that is 20016, so 9744 is abundant (20016 is more than 9744). Euler's totient φ(9744) = 2688 numbers up to 9744 share no factor with it.
- 4
The digits of 9744 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9744 = 2^{4} \times 3 \times 7 \times 29 \]9744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 29760 |
| Euler totient φ(n) | 2688 |
| Square | 94945536 |
| Cube | 925149302784 |
| Square root | 98.711701 (= 4√609) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.744 × |
9744 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and forty-four |
| Binary (base 2) | 10011000010000 |
| Octal (base 8) | 23020 |
| Hexadecimal (base 16) | 2610 |
| Base 3 | 111100220 |
| As time | 9744 seconds = 2 h 42 min 24 s |
Is 9744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9744 ÷ 2 = 4872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9744 ÷ 3 = 3248) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9744 ÷ 4 = 2436) | 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 | Yes (9744 ÷ 6 = 1624) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9744 ÷ 7 = 1392) | 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 | Yes (9744 ÷ 8 = 1218) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9744 ÷ 12 = 812) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9744 a prime number?
No. 9744 = × 3 × 7 × 29, so it is divisible by 2.
What are the factors of 9744?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 56, 58, 84, 87, 112, 116, 168, 174, 203, 232, 336, 348, 406, 464, 609, 696, 812, 1218, 1392, 1624, 2436, 3248, 4872, 9744.
What is 9744 in binary?
10011000010000 (hexadecimal 2610, octal 23020).
What is the square root of 9744?
About 98.7117, exactly 4√609.
Is 9744 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 9744?
9744 is a Harshad number: divisible by its digit sum 24.