The number 9952
9952 is a composite number with 12 divisors. Its prime factorisation is × 311. Divisors (12): 1, 2, 4, 8, 16, 32, 311, 622, 1244, 2488, 4976, 9952.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9952 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9952 is composite. Its prime factorisation is
- 3
The divisors add up to 19656; without 9952 itself that is 9704, so 9952 is deficient (9704 is less than 9952). Euler's totient φ(9952) = 4960 numbers up to 9952 share no factor with it.
- 4
The digits of 9952 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9952 = 2^{5} \times 311 \]9952 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 19656 |
| Euler totient φ(n) | 4960 |
| Square | 99042304 |
| Cube | 985669009408 |
| Square root | 99.759711 (= 4√622) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 91 |
| Scientific notation | 9.952 × |
9952 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and fifty-two |
| Binary (base 2) | 10011011100000 |
| Octal (base 8) | 23340 |
| Hexadecimal (base 16) | 26E0 |
| Base 3 | 111122121 |
| As time | 9952 seconds = 2 h 45 min 52 s |
Is 9952 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9952 ÷ 2 = 4976) | 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 (9952 ÷ 4 = 2488) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (9952 ÷ 8 = 1244) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 8) | 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 9952 a prime number?
No. 9952 = × 311, so it is divisible by 2.
What are the factors of 9952?
1, 2, 4, 8, 16, 32, 311, 622, 1244, 2488, 4976, 9952.
What is 9952 in binary?
10011011100000 (hexadecimal 26E0, octal 23340).
What is the square root of 9952?
About 99.7597, exactly 4√622.
Is 9952 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 9952?
It is a composite number with 12 divisors.