The number 99840
99840 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 13. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30 … 99840.
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How to work it out
- 1
What is special about 99840: a Harshad number: divisible by its digit sum 30.
- 2
99840 is composite. Its prime factorisation is
- 3
The divisors add up to 343728; without 99840 itself that is 243888, so 99840 is abundant (243888 is more than 99840). Euler's totient φ(99840) = 24576 numbers up to 99840 share no factor with it.
- 4
The digits of 99840 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 128 steps to reach 1.
LaTeX source of the formulas on this page
\[ 99840 = 2^{9} \times 3 \times 5 \times 13 \]99840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 343728 |
| Euler totient φ(n) | 24576 |
| Square | 9968025600 |
| Cube | 995207675904000 |
| Square root | 315.974683 (= 16√390) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 128 |
| Scientific notation | 9.984 × |
99840 in other forms
| Form | Value |
|---|---|
| In words | ninety-nine thousand eight hundred and forty |
| Binary (base 2) | 11000011000000000 |
| Octal (base 8) | 303000 |
| Hexadecimal (base 16) | 18600 |
| Base 3 | 12001221210 |
| As time | 99840 seconds = 27 h 44 min 0 s |
Is 99840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (99840 ÷ 2 = 49920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (99840 ÷ 3 = 33280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (99840 ÷ 4 = 24960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (99840 ÷ 5 = 19968) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (99840 ÷ 6 = 16640) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (99840 ÷ 8 = 12480) | 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 (99840 ÷ 10 = 9984) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (99840 ÷ 12 = 8320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 99840 a prime number?
No. 99840 = × 3 × 5 × 13, so it is divisible by 2.
What are the factors of 99840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60, 64, 65, 78, 80, 96, 104, 120, 128, 130, 156, 160, 192, 195, 208, 240, 256, 260, 312, 320, 384, 390, 416, 480, 512, 520, 624, 640, 768, 780, 832, 960, 1040, 1248, 1280, 1536, 1560, 1664, 1920, 2080, 2496, 2560, 3120, 3328, 3840, 4160, 4992, 6240, 6656, 7680, 8320, 9984, 12480, 16640, 19968, 24960, 33280, 49920, 99840.
What is 99840 in binary?
11000011000000000 (hexadecimal 18600, octal 303000).
What is the square root of 99840?
About 315.9747, exactly 16√390.
Is 99840 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 99840?
99840 is a Harshad number: divisible by its digit sum 30.