The number 27840
27840 is a composite number with 56 divisors. Its prime factorisation is × 3 × 5 × 29. Divisors (56): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32 … 27840.
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How to work it out
- 1
What is special about 27840: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27840 is composite. Its prime factorisation is
- 3
The divisors add up to 91440; without 27840 itself that is 63600, so 27840 is abundant (63600 is more than 27840). Euler's totient φ(27840) = 7168 numbers up to 27840 share no factor with it.
- 4
The digits of 27840 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 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27840 = 2^{6} \times 3 \times 5 \times 29 \]27840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 91440 |
| Euler totient φ(n) | 7168 |
| Square | 775065600 |
| Cube | 21577826304000 |
| Square root | 166.853229 (= 8√435) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 33 |
| Scientific notation | 2.784 × |
27840 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand eight hundred and forty |
| Binary (base 2) | 110110011000000 |
| Octal (base 8) | 66300 |
| Hexadecimal (base 16) | 6CC0 |
| Base 3 | 1102012010 |
| As time | 27840 seconds = 7 h 44 min 0 s |
Is 27840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27840 ÷ 2 = 13920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27840 ÷ 3 = 9280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27840 ÷ 4 = 6960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27840 ÷ 5 = 5568) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27840 ÷ 6 = 4640) | 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 (27840 ÷ 8 = 3480) | 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 (27840 ÷ 10 = 2784) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27840 ÷ 12 = 2320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27840 a prime number?
No. 27840 = × 3 × 5 × 29, so it is divisible by 2.
What are the factors of 27840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80, 87, 96, 116, 120, 145, 160, 174, 192, 232, 240, 290, 320, 348, 435, 464, 480, 580, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 2320, 2784, 3480, 4640, 5568, 6960, 9280, 13920, 27840.
What is 27840 in binary?
110110011000000 (hexadecimal 6CC0, octal 66300).
What is the square root of 27840?
About 166.8532, exactly 8√435.
Is 27840 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27840?
27840 is a happy number: repeatedly adding the squares of its digits reaches 1.