The number 9984
9984 is a composite number with 36 divisors. Its prime factorisation is × 3 × 13. Divisors (36): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64 … 9984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9984 is composite. Its prime factorisation is
- 3
The divisors add up to 28616; without 9984 itself that is 18632, so 9984 is abundant (18632 is more than 9984). Euler's totient φ(9984) = 3072 numbers up to 9984 share no factor with it.
- 4
The digits of 9984 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9984 = 2^{8} \times 3 \times 13 \]9984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 28616 |
| Euler totient φ(n) | 3072 |
| Square | 99680256 |
| Cube | 995207675904 |
| Square root | 99.919968 (= 16√39) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 9.984 × |
9984 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and eighty-four |
| Binary (base 2) | 10011100000000 |
| Octal (base 8) | 23400 |
| Hexadecimal (base 16) | 2700 |
| Base 3 | 111200210 |
| As time | 9984 seconds = 2 h 46 min 24 s |
Is 9984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9984 ÷ 2 = 4992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9984 ÷ 3 = 3328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9984 ÷ 4 = 2496) | 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 (9984 ÷ 6 = 1664) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (9984 ÷ 8 = 1248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9984 ÷ 12 = 832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9984 a prime number?
No. 9984 = × 3 × 13, so it is divisible by 2.
What are the factors of 9984?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984.
What is 9984 in binary?
10011100000000 (hexadecimal 2700, octal 23400).
What is the square root of 9984?
About 99.9200, exactly 16√39.
Is 9984 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9984?
It is a composite number with 36 divisors.