The number 27384
27384 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 163. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 163 … 27384.
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How to work it out
- 1
What is special about 27384: a Harshad number: divisible by its digit sum 24.
- 2
27384 is composite. Its prime factorisation is
- 3
The divisors add up to 78720; without 27384 itself that is 51336, so 27384 is abundant (51336 is more than 27384). Euler's totient φ(27384) = 7776 numbers up to 27384 share no factor with it.
- 4
The digits of 27384 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 152 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27384 = 2^{3} \times 3 \times 7 \times 163 \]27384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 78720 |
| Euler totient φ(n) | 7776 |
| Square | 749883456 |
| Cube | 20534808559104 |
| Square root | 165.481117 (= 2√6846) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.7384 × |
27384 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand three hundred and eighty-four |
| Binary (base 2) | 110101011111000 |
| Octal (base 8) | 65370 |
| Hexadecimal (base 16) | 6AF8 |
| Base 3 | 1101120020 |
| As time | 27384 seconds = 7 h 36 min 24 s |
Is 27384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27384 ÷ 2 = 13692) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27384 ÷ 3 = 9128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27384 ÷ 4 = 6846) | 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 (27384 ÷ 6 = 4564) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27384 ÷ 7 = 3912) | 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 (27384 ÷ 8 = 3423) | 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 | No (remainder 4) | 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 (27384 ÷ 12 = 2282) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27384 a prime number?
No. 27384 = × 3 × 7 × 163, so it is divisible by 2.
What are the factors of 27384?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 163, 168, 326, 489, 652, 978, 1141, 1304, 1956, 2282, 3423, 3912, 4564, 6846, 9128, 13692, 27384.
What is 27384 in binary?
110101011111000 (hexadecimal 6AF8, octal 65370).
What is the square root of 27384?
About 165.4811, exactly 2√6846.
Is 27384 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 27384?
27384 is a Harshad number: divisible by its digit sum 24.