The number 9864
9864 is a composite number with 24 divisors. Its prime factorisation is × × 137. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 137, 274, 411, 548 … 9864.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9864 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9864 is composite. Its prime factorisation is
- 3
The divisors add up to 26910; without 9864 itself that is 17046, so 9864 is abundant (17046 is more than 9864). Euler's totient φ(9864) = 3264 numbers up to 9864 share no factor with it.
- 4
The digits of 9864 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9864 = 2^{3} \times 3^{2} \times 137 \]9864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 26910 |
| Euler totient φ(n) | 3264 |
| Square | 97298496 |
| Cube | 959752364544 |
| Square root | 99.317672 (= 6√274) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.864 × |
9864 in other forms
| Form | Value |
|---|---|
| In words | nine thousand eight hundred and sixty-four |
| Binary (base 2) | 10011010001000 |
| Octal (base 8) | 23210 |
| Hexadecimal (base 16) | 2688 |
| Base 3 | 111112100 |
| As time | 9864 seconds = 2 h 44 min 24 s |
Is 9864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9864 ÷ 2 = 4932) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9864 ÷ 3 = 3288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9864 ÷ 4 = 2466) | 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 (9864 ÷ 6 = 1644) | 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 (9864 ÷ 8 = 1233) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9864 ÷ 9 = 1096) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9864 ÷ 12 = 822) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9864 a prime number?
No. 9864 = × × 137, so it is divisible by 2.
What are the factors of 9864?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 137, 274, 411, 548, 822, 1096, 1233, 1644, 2466, 3288, 4932, 9864.
What is 9864 in binary?
10011010001000 (hexadecimal 2688, octal 23210).
What is the square root of 9864?
About 99.3177, exactly 6√274.
Is 9864 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9864?
It is a composite number with 24 divisors.