The number 32880
32880 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 137. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 32880.
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How to work it out
- 1
32880 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32880 is composite. Its prime factorisation is
- 3
The divisors add up to 102672; without 32880 itself that is 69792, so 32880 is abundant (69792 is more than 32880). Euler's totient φ(32880) = 8704 numbers up to 32880 share no factor with it.
- 4
The digits of 32880 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32880 = 2^{4} \times 3 \times 5 \times 137 \]32880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 102672 |
| Euler totient φ(n) | 8704 |
| Square | 1081094400 |
| Cube | 35546383872000 |
| Square root | 181.328431 (= 4√2055) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.288 × |
32880 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand eight hundred and eighty |
| Binary (base 2) | 1000000001110000 |
| Octal (base 8) | 100160 |
| Hexadecimal (base 16) | 8070 |
| Base 3 | 1200002210 |
| As time | 32880 seconds = 9 h 8 min 0 s |
Is 32880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32880 ÷ 2 = 16440) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32880 ÷ 3 = 10960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32880 ÷ 4 = 8220) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32880 ÷ 5 = 6576) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32880 ÷ 6 = 5480) | 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 | Yes (32880 ÷ 8 = 4110) | 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 | Yes (32880 ÷ 10 = 3288) | 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 | Yes (32880 ÷ 12 = 2740) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32880 a prime number?
No. 32880 = × 3 × 5 × 137, so it is divisible by 2.
What are the factors of 32880?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 137, 240, 274, 411, 548, 685, 822, 1096, 1370, 1644, 2055, 2192, 2740, 3288, 4110, 5480, 6576, 8220, 10960, 16440, 32880.
What is 32880 in binary?
1000000001110000 (hexadecimal 8070, octal 100160).
What is the square root of 32880?
About 181.3284, exactly 4√2055.
Is 32880 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 32880?
It is a composite number with 40 divisors.