The number 9752
9752 is a composite number with 16 divisors. Its prime factorisation is × 23 × 53. Divisors (16): 1, 2, 4, 8, 23, 46, 53, 92, 106, 184, 212, 424, 1219, 2438, 4876, 9752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9752: a Harshad number: divisible by its digit sum 23.
- 2
9752 is composite. Its prime factorisation is
- 3
The divisors add up to 19440; without 9752 itself that is 9688, so 9752 is deficient (9688 is less than 9752). Euler's totient φ(9752) = 4576 numbers up to 9752 share no factor with it.
- 4
The digits of 9752 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9752 = 2^{3} \times 23 \times 53 \]9752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 19440 |
| Euler totient φ(n) | 4576 |
| Square | 95101504 |
| Cube | 927429867008 |
| Square root | 98.752215 (= 2√2438) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.752 × |
9752 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and fifty-two |
| Binary (base 2) | 10011000011000 |
| Octal (base 8) | 23030 |
| Hexadecimal (base 16) | 2618 |
| Base 3 | 111101012 |
| As time | 9752 seconds = 2 h 42 min 32 s |
Is 9752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9752 ÷ 2 = 4876) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9752 ÷ 4 = 2438) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | Yes (9752 ÷ 8 = 1219) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9752 a prime number?
No. 9752 = × 23 × 53, so it is divisible by 2.
What are the factors of 9752?
1, 2, 4, 8, 23, 46, 53, 92, 106, 184, 212, 424, 1219, 2438, 4876, 9752.
What is 9752 in binary?
10011000011000 (hexadecimal 2618, octal 23030).
What is the square root of 9752?
About 98.7522, exactly 2√2438.
Is 9752 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 9752?
9752 is a Harshad number: divisible by its digit sum 23.