The number 10406
10406 is a composite number with 12 divisors. Its prime factorisation is 2 × × 43. Divisors (12): 1, 2, 11, 22, 43, 86, 121, 242, 473, 946, 5203, 10406.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10406: a Harshad number: divisible by its digit sum 11.
- 2
10406 is composite. Its prime factorisation is
- 3
The divisors add up to 17556; without 10406 itself that is 7150, so 10406 is deficient (7150 is less than 10406). Euler's totient φ(10406) = 4620 numbers up to 10406 share no factor with it.
- 4
The digits of 10406 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10406 = 2 \times 11^{2} \times 43 \]10406 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 17556 |
| Euler totient φ(n) | 4620 |
| Square | 108284836 |
| Cube | 1126812003416 |
| Square root | 102.009803 (= 11√86) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0406 × |
10406 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and six |
| Binary (base 2) | 10100010100110 |
| Octal (base 8) | 24246 |
| Hexadecimal (base 16) | 28A6 |
| Base 3 | 112021102 |
| As time | 10406 seconds = 2 h 53 min 26 s |
Is 10406 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10406 ÷ 2 = 5203) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 2) | 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 | Yes (10406 ÷ 11 = 946) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10406 a prime number?
No. 10406 = 2 × × 43, so it is divisible by 2.
What are the factors of 10406?
1, 2, 11, 22, 43, 86, 121, 242, 473, 946, 5203, 10406.
What is 10406 in binary?
10100010100110 (hexadecimal 28A6, octal 24246).
What is the square root of 10406?
About 102.0098, exactly 11√86.
Is 10406 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 10406?
10406 is a Harshad number: divisible by its digit sum 11.