The number 32800
32800 is a composite number with 36 divisors. Its prime factorisation is × × 41. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 41, 50, 80, 82, 100 … 32800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
32800 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32800 is composite. Its prime factorisation is
- 3
The divisors add up to 82026; without 32800 itself that is 49226, so 32800 is abundant (49226 is more than 32800). Euler's totient φ(32800) = 12800 numbers up to 32800 share no factor with it.
- 4
The digits of 32800 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32800 = 2^{5} \times 5^{2} \times 41 \]32800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 82026 |
| Euler totient φ(n) | 12800 |
| Square | 1075840000 |
| Cube | 35287552000000 |
| Square root | 181.107703 (= 20√82) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.28 × |
32800 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand eight hundred |
| Binary (base 2) | 1000000000100000 |
| Octal (base 8) | 100040 |
| Hexadecimal (base 16) | 8020 |
| Base 3 | 1122222211 |
| As time | 32800 seconds = 9 h 6 min 40 s |
Is 32800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32800 ÷ 2 = 16400) | 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 (32800 ÷ 4 = 8200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32800 ÷ 5 = 6560) | 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 | No (remainder 5) | 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 (32800 ÷ 8 = 4100) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32800 ÷ 10 = 3280) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 32800 a prime number?
No. 32800 = × × 41, so it is divisible by 2.
What are the factors of 32800?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 41, 50, 80, 82, 100, 160, 164, 200, 205, 328, 400, 410, 656, 800, 820, 1025, 1312, 1640, 2050, 3280, 4100, 6560, 8200, 16400, 32800.
What is 32800 in binary?
1000000000100000 (hexadecimal 8020, octal 100040).
What is the square root of 32800?
About 181.1077, exactly 20√82.
Is 32800 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 32800?
It is a composite number with 36 divisors.