The number 32640
32640 is a triangular number: 1 + 2 + … + 255 = 32640. Its prime factorisation is × 3 × 5 × 17. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32 … 32640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32640: a triangular number: 1 + 2 + … + 255 = 32640; a Harshad number: divisible by its digit sum 15.
- 2
32640 is composite. Its prime factorisation is
- 3
The divisors add up to 110160; without 32640 itself that is 77520, so 32640 is abundant (77520 is more than 32640). Euler's totient φ(32640) = 8192 numbers up to 32640 share no factor with it.
- 4
The digits of 32640 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32640 = 2^{7} \times 3 \times 5 \times 17 \]32640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 110160 |
| Euler totient φ(n) | 8192 |
| Square | 1065369600 |
| Cube | 34773663744000 |
| Square root | 180.665437 (= 8√510) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.264 × |
32640 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand six hundred and forty |
| Binary (base 2) | 111111110000000 |
| Octal (base 8) | 77600 |
| Hexadecimal (base 16) | 7F80 |
| Base 3 | 1122202220 |
| As time | 32640 seconds = 9 h 4 min 0 s |
Is 32640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32640 ÷ 2 = 16320) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32640 ÷ 3 = 10880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32640 ÷ 4 = 8160) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32640 ÷ 5 = 6528) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32640 ÷ 6 = 5440) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (32640 ÷ 8 = 4080) | 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 (32640 ÷ 10 = 3264) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32640 ÷ 12 = 2720) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32640 a prime number?
No. 32640 = × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 32640?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 272, 320, 340, 384, 408, 480, 510, 544, 640, 680, 816, 960, 1020, 1088, 1360, 1632, 1920, 2040, 2176, 2720, 3264, 4080, 5440, 6528, 8160, 10880, 16320, 32640.
What is 32640 in binary?
111111110000000 (hexadecimal 7F80, octal 77600).
What is the square root of 32640?
About 180.6654, exactly 8√510.
Is 32640 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 32640?
32640 is a triangular number: 1 + 2 + … + 255 = 32640; a Harshad number: divisible by its digit sum 15.