The number 27405
27405 is a composite number with 32 divisors. Its prime factorisation is × 5 × 7 × 29. Divisors (32): 1, 3, 5, 7, 9, 15, 21, 27, 29, 35, 45, 63, 87, 105, 135, 145 … 27405.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27405: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27405 is composite. Its prime factorisation is
- 3
The divisors add up to 57600; without 27405 itself that is 30195, so 27405 is abundant (30195 is more than 27405). Euler's totient φ(27405) = 12096 numbers up to 27405 share no factor with it.
- 4
The digits of 27405 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 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27405 = 3^{3} \times 5 \times 7 \times 29 \]27405 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 57600 |
| Euler totient φ(n) | 12096 |
| Square | 751034025 |
| Cube | 20582087455125 |
| Square root | 165.544556 (= 3√3045) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.7405 × |
27405 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand four hundred and five |
| Binary (base 2) | 110101100001101 |
| Octal (base 8) | 65415 |
| Hexadecimal (base 16) | 6B0D |
| Base 3 | 1101121000 |
| As time | 27405 seconds = 7 h 36 min 45 s |
Is 27405 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27405 ÷ 3 = 9135) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27405 ÷ 5 = 5481) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27405 ÷ 7 = 3915) | 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27405 ÷ 9 = 3045) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27405 a prime number?
No. 27405 = × 5 × 7 × 29, so it is divisible by 3.
What are the factors of 27405?
1, 3, 5, 7, 9, 15, 21, 27, 29, 35, 45, 63, 87, 105, 135, 145, 189, 203, 261, 315, 435, 609, 783, 945, 1015, 1305, 1827, 3045, 3915, 5481, 9135, 27405.
What is 27405 in binary?
110101100001101 (hexadecimal 6B0D, octal 65415).
What is the square root of 27405?
About 165.5446, exactly 3√3045.
Is 27405 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27405?
27405 is a happy number: repeatedly adding the squares of its digits reaches 1.