The number 406
406 is a triangular number: 1 + 2 + … + 28 = 406. Its prime factorisation is 2 × 7 × 29. Divisors (8): 1, 2, 7, 14, 29, 58, 203, 406.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 406: a triangular number: 1 + 2 + … + 28 = 406.
- 2
406 is composite. Its prime factorisation is
- 3
The divisors add up to 720; without 406 itself that is 314, so 406 is deficient (314 is less than 406). Euler's totient φ(406) = 168 numbers up to 406 share no factor with it.
- 4
The digits of 406 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 406 = 2 \times 7 \times 29 \]
406 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 720 |
| Euler totient φ(n) | 168 |
| Square | 164836 |
| Cube | 66923416 |
| Square root | 20.149442 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 40 |
| Scientific notation | 4.06 × |
406 in other forms
| Form | Value |
|---|---|
| In words | four hundred and six |
| Roman numerals | CDVI |
| Binary (base 2) | 110010110 |
| Octal (base 8) | 626 |
| Hexadecimal (base 16) | 196 |
| Base 3 | 120001 |
| As time | 406 seconds = 6 min 46 s |
Is 406 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (406 ÷ 2 = 203) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (406 ÷ 7 = 58) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 406 a prime number?
No. 406 = 2 × 7 × 29, so it is divisible by 2.
What are the factors of 406?
1, 2, 7, 14, 29, 58, 203, 406.
What is 406 in binary?
110010110 (hexadecimal 196, octal 626).
What is the square root of 406?
About 20.1494.
What is 406 in Roman numerals?
CDVI.
Is 406 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 406?
406 is a triangular number: 1 + 2 + … + 28 = 406.