The number 32760
32760 is a composite number with 96 divisors. Its prime factorisation is × × 5 × 7 × 13. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20 … 32760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32760: a Harshad number: divisible by its digit sum 18.
- 2
32760 is composite. Its prime factorisation is
- 3
The divisors add up to 131040; without 32760 itself that is 98280, so 32760 is abundant (98280 is more than 32760). Euler's totient φ(32760) = 6912 numbers up to 32760 share no factor with it.
- 4
The digits of 32760 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32760 = 2^{3} \times 3^{2} \times 5 \times 7 \times 13 \]32760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 131040 |
| Euler totient φ(n) | 6912 |
| Square | 1073217600 |
| Cube | 35158608576000 |
| Square root | 180.997238 (= 6√910) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.276 × |
32760 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and sixty |
| Binary (base 2) | 111111111111000 |
| Octal (base 8) | 77770 |
| Hexadecimal (base 16) | 7FF8 |
| Base 3 | 1122221100 |
| As time | 32760 seconds = 9 h 6 min 0 s |
Is 32760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32760 ÷ 2 = 16380) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32760 ÷ 3 = 10920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32760 ÷ 4 = 8190) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32760 ÷ 5 = 6552) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32760 ÷ 6 = 5460) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (32760 ÷ 7 = 4680) | 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 (32760 ÷ 8 = 4095) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32760 ÷ 9 = 3640) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32760 ÷ 10 = 3276) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32760 ÷ 12 = 2730) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32760 a prime number?
No. 32760 = × × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 32760?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 26, 28, 30, 35, 36, 39, 40, 42, 45, 52, 56, 60, 63, 65, 70, 72, 78, 84, 90, 91, 104, 105, 117, 120, 126, 130, 140, 156, 168, 180, 182, 195, 210, 234, 252, 260, 273, 280, 312, 315, 360, 364, 390, 420, 455, 468, 504, 520, 546, 585, 630, 728, 780, 819, 840, 910, 936, 1092, 1170, 1260, 1365, 1560, 1638, 1820, 2184, 2340, 2520, 2730, 3276, 3640, 4095, 4680, 5460, 6552, 8190, 10920, 16380, 32760.
What is 32760 in binary?
111111111111000 (hexadecimal 7FF8, octal 77770).
What is the square root of 32760?
About 180.9972, exactly 6√910.
Is 32760 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32760?
32760 is a Harshad number: divisible by its digit sum 18.