The number 32004
32004 is a composite number with 36 divisors. Its prime factorisation is × × 7 × 127. Divisors (36): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84 … 32004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32004: a Harshad number: divisible by its digit sum 9.
- 2
32004 is composite. Its prime factorisation is
- 3
The divisors add up to 93184; without 32004 itself that is 61180, so 32004 is abundant (61180 is more than 32004). Euler's totient φ(32004) = 9072 numbers up to 32004 share no factor with it.
- 4
The digits of 32004 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32004 = 2^{2} \times 3^{2} \times 7 \times 127 \]32004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 93184 |
| Euler totient φ(n) | 9072 |
| Square | 1024256016 |
| Cube | 32780289536064 |
| Square root | 178.896618 (= 6√889) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.2004 × |
32004 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand and four |
| Binary (base 2) | 111110100000100 |
| Octal (base 8) | 76404 |
| Hexadecimal (base 16) | 7D04 |
| Base 3 | 1121220100 |
| As time | 32004 seconds = 8 h 53 min 24 s |
Is 32004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32004 ÷ 2 = 16002) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32004 ÷ 3 = 10668) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32004 ÷ 4 = 8001) | 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 (32004 ÷ 6 = 5334) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (32004 ÷ 7 = 4572) | 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 | Yes (32004 ÷ 9 = 3556) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32004 ÷ 12 = 2667) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32004 a prime number?
No. 32004 = × × 7 × 127, so it is divisible by 2.
What are the factors of 32004?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 127, 252, 254, 381, 508, 762, 889, 1143, 1524, 1778, 2286, 2667, 3556, 4572, 5334, 8001, 10668, 16002, 32004.
What is 32004 in binary?
111110100000100 (hexadecimal 7D04, octal 76404).
What is the square root of 32004?
About 178.8966, exactly 6√889.
Is 32004 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 32004?
32004 is a Harshad number: divisible by its digit sum 9.