The number 408
408 is a composite number with 16 divisors. Its prime factorisation is × 3 × 17. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 408: a Harshad number: divisible by its digit sum 12.
- 2
408 is composite. Its prime factorisation is
- 3
The divisors add up to 1080; without 408 itself that is 672, so 408 is abundant (672 is more than 408). Euler's totient φ(408) = 128 numbers up to 408 share no factor with it.
- 4
The digits of 408 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 408 = 2^{3} \times 3 \times 17 \]408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 1080 |
| Euler totient φ(n) | 128 |
| Square | 166464 |
| Cube | 67917312 |
| Square root | 20.199010 (= 2√102) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 27 |
| Scientific notation | 4.08 × |
408 in other forms
| Form | Value |
|---|---|
| In words | four hundred and eight |
| Roman numerals | CDVIII |
| Binary (base 2) | 110011000 |
| Octal (base 8) | 630 |
| Hexadecimal (base 16) | 198 |
| Base 3 | 120010 |
| As time | 408 seconds = 6 min 48 s |
Is 408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (408 ÷ 2 = 204) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (408 ÷ 3 = 136) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (408 ÷ 4 = 102) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (408 ÷ 6 = 68) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (408 ÷ 8 = 51) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (408 ÷ 12 = 34) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 408 a prime number?
No. 408 = × 3 × 17, so it is divisible by 2.
What are the factors of 408?
1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.
What is 408 in binary?
110011000 (hexadecimal 198, octal 630).
What is the square root of 408?
About 20.1990, exactly 2√102.
What is 408 in Roman numerals?
CDVIII.
Is 408 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 408?
408 is a Harshad number: divisible by its digit sum 12.