The number 15840
15840 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 15840.
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How to work it out
- 1
What is special about 15840: a Harshad number: divisible by its digit sum 18.
- 2
15840 is composite. Its prime factorisation is
- 3
The divisors add up to 58968; without 15840 itself that is 43128, so 15840 is abundant (43128 is more than 15840). Euler's totient φ(15840) = 3840 numbers up to 15840 share no factor with it.
- 4
The digits of 15840 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 102 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15840 = 2^{5} \times 3^{2} \times 5 \times 11 \]15840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 58968 |
| Euler totient φ(n) | 3840 |
| Square | 250905600 |
| Cube | 3974344704000 |
| Square root | 125.857062 (= 12√110) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 102 |
| Scientific notation | 1.584 × |
15840 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand eight hundred and forty |
| Binary (base 2) | 11110111100000 |
| Octal (base 8) | 36740 |
| Hexadecimal (base 16) | 3DE0 |
| Base 3 | 210201200 |
| As time | 15840 seconds = 4 h 24 min 0 s |
Is 15840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15840 ÷ 2 = 7920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15840 ÷ 3 = 5280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15840 ÷ 4 = 3960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (15840 ÷ 5 = 3168) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (15840 ÷ 6 = 2640) | 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 (15840 ÷ 8 = 1980) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (15840 ÷ 9 = 1760) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (15840 ÷ 10 = 1584) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (15840 ÷ 11 = 1440) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15840 ÷ 12 = 1320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15840 a prime number?
No. 15840 = × × 5 × 11, so it is divisible by 2.
What are the factors of 15840?
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 32, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 96, 99, 110, 120, 132, 144, 160, 165, 176, 180, 198, 220, 240, 264, 288, 330, 352, 360, 396, 440, 480, 495, 528, 660, 720, 792, 880, 990, 1056, 1320, 1440, 1584, 1760, 1980, 2640, 3168, 3960, 5280, 7920, 15840.
What is 15840 in binary?
11110111100000 (hexadecimal 3DE0, octal 36740).
What is the square root of 15840?
About 125.8571, exactly 12√110.
Is 15840 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 15840?
15840 is a Harshad number: divisible by its digit sum 18.