The number 21840
21840 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7 × 13. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21 … 21840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21840: a Harshad number: divisible by its digit sum 15.
- 2
21840 is composite. Its prime factorisation is
- 3
The divisors add up to 83328; without 21840 itself that is 61488, so 21840 is abundant (61488 is more than 21840). Euler's totient φ(21840) = 4608 numbers up to 21840 share no factor with it.
- 4
The digits of 21840 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21840 = 2^{4} \times 3 \times 5 \times 7 \times 13 \]21840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 83328 |
| Euler totient φ(n) | 4608 |
| Square | 476985600 |
| Cube | 10417365504000 |
| Square root | 147.783626 (= 4√1365) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 17 |
| Scientific notation | 2.184 × |
21840 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand eight hundred and forty |
| Binary (base 2) | 101010101010000 |
| Octal (base 8) | 52520 |
| Hexadecimal (base 16) | 5550 |
| Base 3 | 1002221220 |
| As time | 21840 seconds = 6 h 4 min 0 s |
Is 21840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21840 ÷ 2 = 10920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21840 ÷ 3 = 7280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21840 ÷ 4 = 5460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21840 ÷ 5 = 4368) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21840 ÷ 6 = 3640) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (21840 ÷ 7 = 3120) | 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 (21840 ÷ 8 = 2730) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21840 ÷ 10 = 2184) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21840 ÷ 12 = 1820) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21840 a prime number?
No. 21840 = × 3 × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 21840?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21, 24, 26, 28, 30, 35, 39, 40, 42, 48, 52, 56, 60, 65, 70, 78, 80, 84, 91, 104, 105, 112, 120, 130, 140, 156, 168, 182, 195, 208, 210, 240, 260, 273, 280, 312, 336, 364, 390, 420, 455, 520, 546, 560, 624, 728, 780, 840, 910, 1040, 1092, 1365, 1456, 1560, 1680, 1820, 2184, 2730, 3120, 3640, 4368, 5460, 7280, 10920, 21840.
What is 21840 in binary?
101010101010000 (hexadecimal 5550, octal 52520).
What is the square root of 21840?
About 147.7836, exactly 4√1365.
Is 21840 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 21840?
21840 is a Harshad number: divisible by its digit sum 15.