The number 404
404 is a palindrome: it reads 404 backwards too. Its prime factorisation is × 101. Divisors (6): 1, 2, 4, 101, 202, 404.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 404: a palindrome: it reads 404 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
404 is composite. Its prime factorisation is
- 3
The divisors add up to 714; without 404 itself that is 310, so 404 is deficient (310 is less than 404). Euler's totient φ(404) = 200 numbers up to 404 share no factor with it.
- 4
The digits of 404 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 404 = 2^{2} \times 101 \]404 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 714 |
| Euler totient φ(n) | 200 |
| Square | 163216 |
| Cube | 65939264 |
| Square root | 20.099751 (= 2√101) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 27 |
| Scientific notation | 4.04 × |
404 in other forms
| Form | Value |
|---|---|
| In words | four hundred and four |
| Roman numerals | CDIV |
| Binary (base 2) | 110010100 |
| Octal (base 8) | 624 |
| Hexadecimal (base 16) | 194 |
| Base 3 | 112222 |
| As time | 404 seconds = 6 min 44 s |
Is 404 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (404 ÷ 2 = 202) | 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 | Yes (404 ÷ 4 = 101) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 8) | 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 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 404 a prime number?
No. 404 = × 101, so it is divisible by 2.
What are the factors of 404?
1, 2, 4, 101, 202, 404.
What is 404 in binary?
110010100 (hexadecimal 194, octal 624).
What is the square root of 404?
About 20.0998, exactly 2√101.
What is 404 in Roman numerals?
CDIV.
Is 404 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 404?
404 is a palindrome: it reads 404 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.