The number 17840
17840 is a composite number with 20 divisors. Its prime factorisation is × 5 × 223. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 223, 446, 892, 1115, 1784, 2230 … 17840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17840: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 20.
- 2
17840 is composite. Its prime factorisation is
- 3
The divisors add up to 41664; without 17840 itself that is 23824, so 17840 is abundant (23824 is more than 17840). Euler's totient φ(17840) = 7104 numbers up to 17840 share no factor with it.
- 4
The digits of 17840 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 97 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17840 = 2^{4} \times 5 \times 223 \]17840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 41664 |
| Euler totient φ(n) | 7104 |
| Square | 318265600 |
| Cube | 5677858304000 |
| Square root | 133.566463 (= 4√1115) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 97 |
| Scientific notation | 1.784 × |
17840 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand eight hundred and forty |
| Binary (base 2) | 100010110110000 |
| Octal (base 8) | 42660 |
| Hexadecimal (base 16) | 45B0 |
| Base 3 | 220110202 |
| As time | 17840 seconds = 4 h 57 min 20 s |
Is 17840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17840 ÷ 2 = 8920) | 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 (17840 ÷ 4 = 4460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17840 ÷ 5 = 3568) | 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 4) | 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 (17840 ÷ 8 = 2230) | 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 | Yes (17840 ÷ 10 = 1784) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 17840 a prime number?
No. 17840 = × 5 × 223, so it is divisible by 2.
What are the factors of 17840?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 223, 446, 892, 1115, 1784, 2230, 3568, 4460, 8920, 17840.
What is 17840 in binary?
100010110110000 (hexadecimal 45B0, octal 42660).
What is the square root of 17840?
About 133.5665, exactly 4√1115.
Is 17840 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 17840?
17840 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 20.