The number 32320
32320 is a composite number with 28 divisors. Its prime factorisation is × 5 × 101. Divisors (28): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 101, 160, 202, 320 … 32320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32320: a Harshad number: divisible by its digit sum 10.
- 2
32320 is composite. Its prime factorisation is
- 3
The divisors add up to 77724; without 32320 itself that is 45404, so 32320 is abundant (45404 is more than 32320). Euler's totient φ(32320) = 12800 numbers up to 32320 share no factor with it.
- 4
The digits of 32320 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32320 = 2^{6} \times 5 \times 101 \]32320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 77724 |
| Euler totient φ(n) | 12800 |
| Square | 1044582400 |
| Cube | 33760903168000 |
| Square root | 179.777640 (= 8√505) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.232 × |
32320 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand three hundred and twenty |
| Binary (base 2) | 111111001000000 |
| Octal (base 8) | 77100 |
| Hexadecimal (base 16) | 7E40 |
| Base 3 | 1122100001 |
| As time | 32320 seconds = 8 h 58 min 40 s |
Is 32320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32320 ÷ 2 = 16160) | 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 (32320 ÷ 4 = 8080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32320 ÷ 5 = 6464) | 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 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 (32320 ÷ 8 = 4040) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32320 ÷ 10 = 3232) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32320 a prime number?
No. 32320 = × 5 × 101, so it is divisible by 2.
What are the factors of 32320?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 101, 160, 202, 320, 404, 505, 808, 1010, 1616, 2020, 3232, 4040, 6464, 8080, 16160, 32320.
What is 32320 in binary?
111111001000000 (hexadecimal 7E40, octal 77100).
What is the square root of 32320?
About 179.7776, exactly 8√505.
Is 32320 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 32320?
32320 is a Harshad number: divisible by its digit sum 10.