The number 32704
32704 is a composite number with 28 divisors. Its prime factorisation is × 7 × 73. Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 73, 112, 146, 224, 292 … 32704.
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How to work it out
- 1
What is special about 32704: a Harshad number: divisible by its digit sum 16.
- 2
32704 is composite. Its prime factorisation is
- 3
The divisors add up to 75184; without 32704 itself that is 42480, so 32704 is abundant (42480 is more than 32704). Euler's totient φ(32704) = 13824 numbers up to 32704 share no factor with it.
- 4
The digits of 32704 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32704 = 2^{6} \times 7 \times 73 \]32704 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 75184 |
| Euler totient φ(n) | 13824 |
| Square | 1069551616 |
| Cube | 34978616049664 |
| Square root | 180.842473 (= 8√511) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.2704 × |
32704 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and four |
| Binary (base 2) | 111111111000000 |
| Octal (base 8) | 77700 |
| Hexadecimal (base 16) | 7FC0 |
| Base 3 | 1122212021 |
| As time | 32704 seconds = 9 h 5 min 4 s |
Is 32704 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32704 ÷ 2 = 16352) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32704 ÷ 4 = 8176) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (32704 ÷ 7 = 4672) | 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 (32704 ÷ 8 = 4088) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32704 a prime number?
No. 32704 = × 7 × 73, so it is divisible by 2.
What are the factors of 32704?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 73, 112, 146, 224, 292, 448, 511, 584, 1022, 1168, 2044, 2336, 4088, 4672, 8176, 16352, 32704.
What is 32704 in binary?
111111111000000 (hexadecimal 7FC0, octal 77700).
What is the square root of 32704?
About 180.8425, exactly 8√511.
Is 32704 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 32704?
32704 is a Harshad number: divisible by its digit sum 16.