The number 8404
8404 is a composite number with 12 divisors. Its prime factorisation is × 11 × 191. Divisors (12): 1, 2, 4, 11, 22, 44, 191, 382, 764, 2101, 4202, 8404.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
8404 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
8404 is composite. Its prime factorisation is
- 3
The divisors add up to 16128; without 8404 itself that is 7724, so 8404 is deficient (7724 is less than 8404). Euler's totient φ(8404) = 3800 numbers up to 8404 share no factor with it.
- 4
The digits of 8404 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8404 = 2^{2} \times 11 \times 191 \]8404 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16128 |
| Euler totient φ(n) | 3800 |
| Square | 70627216 |
| Cube | 593551123264 |
| Square root | 91.673333 (= 2√2101) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 34 |
| Scientific notation | 8.404 × |
8404 in other forms
| Form | Value |
|---|---|
| In words | eight thousand four hundred and four |
| Binary (base 2) | 10000011010100 |
| Octal (base 8) | 20324 |
| Hexadecimal (base 16) | 20D4 |
| Base 3 | 102112021 |
| As time | 8404 seconds = 2 h 20 min 4 s |
Is 8404 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8404 ÷ 2 = 4202) | 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 | Yes (8404 ÷ 4 = 2101) | 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 | No (remainder 4) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | Yes (8404 ÷ 11 = 764) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8404 a prime number?
No. 8404 = × 11 × 191, so it is divisible by 2.
What are the factors of 8404?
1, 2, 4, 11, 22, 44, 191, 382, 764, 2101, 4202, 8404.
What is 8404 in binary?
10000011010100 (hexadecimal 20D4, octal 20324).
What is the square root of 8404?
About 91.6733, exactly 2√2101.
Is 8404 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 8404?
It is a composite number with 12 divisors.