The number 13408
13408 is a composite number with 12 divisors. Its prime factorisation is × 419. Divisors (12): 1, 2, 4, 8, 16, 32, 419, 838, 1676, 3352, 6704, 13408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13408: a Harshad number: divisible by its digit sum 16.
- 2
13408 is composite. Its prime factorisation is
- 3
The divisors add up to 26460; without 13408 itself that is 13052, so 13408 is deficient (13052 is less than 13408). Euler's totient φ(13408) = 6688 numbers up to 13408 share no factor with it.
- 4
The digits of 13408 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13408 = 2^{5} \times 419 \]13408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 26460 |
| Euler totient φ(n) | 6688 |
| Square | 179774464 |
| Cube | 2410416013312 |
| Square root | 115.792919 (= 4√838) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3408 × |
13408 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred and eight |
| Binary (base 2) | 11010001100000 |
| Octal (base 8) | 32140 |
| Hexadecimal (base 16) | 3460 |
| Base 3 | 200101121 |
| As time | 13408 seconds = 3 h 43 min 28 s |
Is 13408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13408 ÷ 2 = 6704) | 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 (13408 ÷ 4 = 3352) | 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 3) | 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 (13408 ÷ 8 = 1676) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 13408 a prime number?
No. 13408 = × 419, so it is divisible by 2.
What are the factors of 13408?
1, 2, 4, 8, 16, 32, 419, 838, 1676, 3352, 6704, 13408.
What is 13408 in binary?
11010001100000 (hexadecimal 3460, octal 32140).
What is the square root of 13408?
About 115.7929, exactly 4√838.
Is 13408 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13408?
13408 is a Harshad number: divisible by its digit sum 16.