The number 1408
1408 is a composite number with 16 divisors. Its prime factorisation is × 11. Divisors (16): 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1408 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1408 is composite. Its prime factorisation is
- 3
The divisors add up to 3060; without 1408 itself that is 1652, so 1408 is abundant (1652 is more than 1408). Euler's totient φ(1408) = 640 numbers up to 1408 share no factor with it.
- 4
The digits of 1408 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1408 = 2^{7} \times 11 \]1408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3060 |
| Euler totient φ(n) | 640 |
| Square | 1982464 |
| Cube | 2791309312 |
| Square root | 37.523326 (= 8√22) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 21 |
| Scientific notation | 1.408 × |
1408 in other forms
| Form | Value |
|---|---|
| In words | one thousand four hundred and eight |
| Roman numerals | MCDVIII |
| Binary (base 2) | 10110000000 |
| Octal (base 8) | 2600 |
| Hexadecimal (base 16) | 580 |
| Base 3 | 1221011 |
| As time | 1408 seconds = 23 min 28 s |
Is 1408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1408 ÷ 2 = 704) | 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 (1408 ÷ 4 = 352) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (1408 ÷ 8 = 176) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 | Yes (1408 ÷ 11 = 128) | 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 1408 a prime number?
No. 1408 = × 11, so it is divisible by 2.
What are the factors of 1408?
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408.
What is 1408 in binary?
10110000000 (hexadecimal 580, octal 2600).
What is the square root of 1408?
About 37.5233, exactly 8√22.
What is 1408 in Roman numerals?
MCDVIII.
Is 1408 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1408?
It is a composite number with 16 divisors.