The number 9840
9840 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 41. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41 … 9840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9840 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9840 is composite. Its prime factorisation is
- 3
The divisors add up to 31248; without 9840 itself that is 21408, so 9840 is abundant (21408 is more than 9840). Euler's totient φ(9840) = 2560 numbers up to 9840 share no factor with it.
- 4
The digits of 9840 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9840 = 2^{4} \times 3 \times 5 \times 41 \]9840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 31248 |
| Euler totient φ(n) | 2560 |
| Square | 96825600 |
| Cube | 952763904000 |
| Square root | 99.196774 (= 4√615) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.84 × |
9840 in other forms
| Form | Value |
|---|---|
| In words | nine thousand eight hundred and forty |
| Binary (base 2) | 10011001110000 |
| Octal (base 8) | 23160 |
| Hexadecimal (base 16) | 2670 |
| Base 3 | 111111110 |
| As time | 9840 seconds = 2 h 44 min 0 s |
Is 9840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9840 ÷ 2 = 4920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9840 ÷ 3 = 3280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9840 ÷ 4 = 2460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9840 ÷ 5 = 1968) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9840 ÷ 6 = 1640) | 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 (9840 ÷ 8 = 1230) | 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 | Yes (9840 ÷ 10 = 984) | 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 | Yes (9840 ÷ 12 = 820) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9840 a prime number?
No. 9840 = × 3 × 5 × 41, so it is divisible by 2.
What are the factors of 9840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920, 9840.
What is 9840 in binary?
10011001110000 (hexadecimal 2670, octal 23160).
What is the square root of 9840?
About 99.1968, exactly 4√615.
Is 9840 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 9840?
It is a composite number with 40 divisors.