The number 27984
27984 is a composite number with 40 divisors. Its prime factorisation is × 3 × 11 × 53. Divisors (40): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 53, 66 … 27984.
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How to work it out
- 1
27984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27984 is composite. Its prime factorisation is
- 3
The divisors add up to 80352; without 27984 itself that is 52368, so 27984 is abundant (52368 is more than 27984). Euler's totient φ(27984) = 8320 numbers up to 27984 share no factor with it.
- 4
The digits of 27984 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 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27984 = 2^{4} \times 3 \times 11 \times 53 \]27984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 80352 |
| Euler totient φ(n) | 8320 |
| Square | 783104256 |
| Cube | 21914389499904 |
| Square root | 167.284189 (= 4√1749) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.7984 × |
27984 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 110110101010000 |
| Octal (base 8) | 66520 |
| Hexadecimal (base 16) | 6D50 |
| Base 3 | 1102101110 |
| As time | 27984 seconds = 7 h 46 min 24 s |
Is 27984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27984 ÷ 2 = 13992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27984 ÷ 3 = 9328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27984 ÷ 4 = 6996) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27984 ÷ 6 = 4664) | 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 (27984 ÷ 8 = 3498) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (27984 ÷ 11 = 2544) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27984 ÷ 12 = 2332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27984 a prime number?
No. 27984 = × 3 × 11 × 53, so it is divisible by 2.
What are the factors of 27984?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 53, 66, 88, 106, 132, 159, 176, 212, 264, 318, 424, 528, 583, 636, 848, 1166, 1272, 1749, 2332, 2544, 3498, 4664, 6996, 9328, 13992, 27984.
What is 27984 in binary?
110110101010000 (hexadecimal 6D50, octal 66520).
What is the square root of 27984?
About 167.2842, exactly 4√1749.
Is 27984 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 27984?
It is a composite number with 40 divisors.