The number 17408
17408 is a composite number with 22 divisors. Its prime factorisation is × 17. Divisors (22): 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544 … 17408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17408: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
17408 is composite. Its prime factorisation is
- 3
The divisors add up to 36846; without 17408 itself that is 19438, so 17408 is abundant (19438 is more than 17408). Euler's totient φ(17408) = 8192 numbers up to 17408 share no factor with it.
- 4
The digits of 17408 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17408 = 2^{10} \times 17 \]17408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 22 |
| Sum of divisors | 36846 |
| Euler totient φ(n) | 8192 |
| Square | 303038464 |
| Cube | 5275293581312 |
| Square root | 131.939380 (= 32√17) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 22 |
| Scientific notation | 1.7408 × |
17408 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand four hundred and eight |
| Binary (base 2) | 100010000000000 |
| Octal (base 8) | 42000 |
| Hexadecimal (base 16) | 4400 |
| Base 3 | 212212202 |
| As time | 17408 seconds = 4 h 50 min 8 s |
Is 17408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17408 ÷ 2 = 8704) | 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 (17408 ÷ 4 = 4352) | 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 6) | 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 (17408 ÷ 8 = 2176) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 6) | 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 17408 a prime number?
No. 17408 = × 17, so it is divisible by 2.
What are the factors of 17408?
1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2176, 4352, 8704, 17408.
What is 17408 in binary?
100010000000000 (hexadecimal 4400, octal 42000).
What is the square root of 17408?
About 131.9394, exactly 32√17.
Is 17408 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 17408?
17408 is a happy number: repeatedly adding the squares of its digits reaches 1.