The number 11408
11408 is a composite number with 20 divisors. Its prime factorisation is × 23 × 31. Divisors (20): 1, 2, 4, 8, 16, 23, 31, 46, 62, 92, 124, 184, 248, 368, 496, 713 … 11408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11408: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
11408 is composite. Its prime factorisation is
- 3
The divisors add up to 23808; without 11408 itself that is 12400, so 11408 is abundant (12400 is more than 11408). Euler's totient φ(11408) = 5280 numbers up to 11408 share no factor with it.
- 4
The digits of 11408 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11408 = 2^{4} \times 23 \times 31 \]11408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 23808 |
| Euler totient φ(n) | 5280 |
| Square | 130142464 |
| Cube | 1484665229312 |
| Square root | 106.808239 (= 4√713) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.1408 × |
11408 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand four hundred and eight |
| Binary (base 2) | 10110010010000 |
| Octal (base 8) | 26220 |
| Hexadecimal (base 16) | 2C90 |
| Base 3 | 120122112 |
| As time | 11408 seconds = 3 h 10 min 8 s |
Is 11408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11408 ÷ 2 = 5704) | 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 (11408 ÷ 4 = 2852) | 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 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 | Yes (11408 ÷ 8 = 1426) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11408 a prime number?
No. 11408 = × 23 × 31, so it is divisible by 2.
What are the factors of 11408?
1, 2, 4, 8, 16, 23, 31, 46, 62, 92, 124, 184, 248, 368, 496, 713, 1426, 2852, 5704, 11408.
What is 11408 in binary?
10110010010000 (hexadecimal 2C90, octal 26220).
What is the square root of 11408?
About 106.8082, exactly 4√713.
Is 11408 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 11408?
11408 is a happy number: repeatedly adding the squares of its digits reaches 1.