The number 17004
17004 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13 × 109. Divisors (24): 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 109, 156, 218, 327, 436 … 17004.
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How to work it out
- 1
What is special about 17004: a Harshad number: divisible by its digit sum 12.
- 2
17004 is composite. Its prime factorisation is
- 3
The divisors add up to 43120; without 17004 itself that is 26116, so 17004 is abundant (26116 is more than 17004). Euler's totient φ(17004) = 5184 numbers up to 17004 share no factor with it.
- 4
The digits of 17004 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 84 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17004 = 2^{2} \times 3 \times 13 \times 109 \]17004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 43120 |
| Euler totient φ(n) | 5184 |
| Square | 289136016 |
| Cube | 4916468816064 |
| Square root | 130.399387 (= 2√4251) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 84 |
| Scientific notation | 1.7004 × |
17004 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand and four |
| Binary (base 2) | 100001001101100 |
| Octal (base 8) | 41154 |
| Hexadecimal (base 16) | 426C |
| Base 3 | 212022210 |
| As time | 17004 seconds = 4 h 43 min 24 s |
Is 17004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17004 ÷ 2 = 8502) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17004 ÷ 3 = 5668) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17004 ÷ 4 = 4251) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17004 ÷ 6 = 2834) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (17004 ÷ 12 = 1417) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17004 a prime number?
No. 17004 = × 3 × 13 × 109, so it is divisible by 2.
What are the factors of 17004?
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 109, 156, 218, 327, 436, 654, 1308, 1417, 2834, 4251, 5668, 8502, 17004.
What is 17004 in binary?
100001001101100 (hexadecimal 426C, octal 41154).
What is the square root of 17004?
About 130.3994, exactly 2√4251.
Is 17004 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 17004?
17004 is a Harshad number: divisible by its digit sum 12.