The number 17340
17340 is a composite number with 36 divisors. Its prime factorisation is × 3 × 5 × . Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68 … 17340.
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How to work it out
- 1
What is special about 17340: a Harshad number: divisible by its digit sum 15.
- 2
17340 is composite. Its prime factorisation is
- 3
The divisors add up to 51576; without 17340 itself that is 34236, so 17340 is abundant (34236 is more than 17340). Euler's totient φ(17340) = 4352 numbers up to 17340 share no factor with it.
- 4
The digits of 17340 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 66 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17340 = 2^{2} \times 3 \times 5 \times 17^{2} \]17340 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 51576 |
| Euler totient φ(n) | 4352 |
| Square | 300675600 |
| Cube | 5213714904000 |
| Square root | 131.681434 (= 34√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 66 |
| Scientific notation | 1.734 × |
17340 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand three hundred and forty |
| Binary (base 2) | 100001110111100 |
| Octal (base 8) | 41674 |
| Hexadecimal (base 16) | 43BC |
| Base 3 | 212210020 |
| As time | 17340 seconds = 4 h 49 min 0 s |
Is 17340 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17340 ÷ 2 = 8670) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17340 ÷ 3 = 5780) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17340 ÷ 4 = 4335) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17340 ÷ 5 = 3468) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17340 ÷ 6 = 2890) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17340 ÷ 10 = 1734) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (17340 ÷ 12 = 1445) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17340 a prime number?
No. 17340 = × 3 × 5 × , so it is divisible by 2.
What are the factors of 17340?
1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 289, 340, 510, 578, 867, 1020, 1156, 1445, 1734, 2890, 3468, 4335, 5780, 8670, 17340.
What is 17340 in binary?
100001110111100 (hexadecimal 43BC, octal 41674).
What is the square root of 17340?
About 131.6814, exactly 34√15.
Is 17340 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 17340?
17340 is a Harshad number: divisible by its digit sum 15.