The number 405
405 is a composite number with 10 divisors. Its prime factorisation is × 5. Divisors (10): 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 405: a Harshad number: divisible by its digit sum 9.
- 2
405 is composite. Its prime factorisation is
- 3
The divisors add up to 726; without 405 itself that is 321, so 405 is deficient (321 is less than 405). Euler's totient φ(405) = 216 numbers up to 405 share no factor with it.
- 4
The digits of 405 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 405 = 3^{4} \times 5 \]405 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 726 |
| Euler totient φ(n) | 216 |
| Square | 164025 |
| Cube | 66430125 |
| Square root | 20.124612 (= 9√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 27 |
| Scientific notation | 4.05 × |
405 in other forms
| Form | Value |
|---|---|
| In words | four hundred and five |
| Roman numerals | CDV |
| Binary (base 2) | 110010101 |
| Octal (base 8) | 625 |
| Hexadecimal (base 16) | 195 |
| Base 3 | 120000 |
| As time | 405 seconds = 6 min 45 s |
Is 405 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 (405 ÷ 3 = 135) | 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 (405 ÷ 5 = 81) | 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 | No (remainder 6) | 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 (405 ÷ 9 = 45) | 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 9) | 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 405 a prime number?
No. 405 = × 5, so it is divisible by 3.
What are the factors of 405?
1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
What is 405 in binary?
110010101 (hexadecimal 195, octal 625).
What is the square root of 405?
About 20.1246, exactly 9√5.
What is 405 in Roman numerals?
CDV.
Is 405 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 405?
405 is a Harshad number: divisible by its digit sum 9.