The number 9924
9924 is a composite number with 12 divisors. Its prime factorisation is × 3 × 827. Divisors (12): 1, 2, 3, 4, 6, 12, 827, 1654, 2481, 3308, 4962, 9924.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9924 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9924 is composite. Its prime factorisation is
- 3
The divisors add up to 23184; without 9924 itself that is 13260, so 9924 is abundant (13260 is more than 9924). Euler's totient φ(9924) = 3304 numbers up to 9924 share no factor with it.
- 4
The digits of 9924 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9924 = 2^{2} \times 3 \times 827 \]9924 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 23184 |
| Euler totient φ(n) | 3304 |
| Square | 98485776 |
| Cube | 977372841024 |
| Square root | 99.619275 (= 2√2481) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 9.924 × |
9924 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and twenty-four |
| Binary (base 2) | 10011011000100 |
| Octal (base 8) | 23304 |
| Hexadecimal (base 16) | 26C4 |
| Base 3 | 111121120 |
| As time | 9924 seconds = 2 h 45 min 24 s |
Is 9924 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9924 ÷ 2 = 4962) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9924 ÷ 3 = 3308) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9924 ÷ 4 = 2481) | 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 (9924 ÷ 6 = 1654) | 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 | No (remainder 4) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9924 ÷ 12 = 827) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9924 a prime number?
No. 9924 = × 3 × 827, so it is divisible by 2.
What are the factors of 9924?
1, 2, 3, 4, 6, 12, 827, 1654, 2481, 3308, 4962, 9924.
What is 9924 in binary?
10011011000100 (hexadecimal 26C4, octal 23304).
What is the square root of 9924?
About 99.6193, exactly 2√2481.
Is 9924 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 9924?
It is a composite number with 12 divisors.