The number 10320
10320 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 43. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43 … 10320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10320: a Harshad number: divisible by its digit sum 6.
- 2
10320 is composite. Its prime factorisation is
- 3
The divisors add up to 32736; without 10320 itself that is 22416, so 10320 is abundant (22416 is more than 10320). Euler's totient φ(10320) = 2688 numbers up to 10320 share no factor with it.
- 4
The digits of 10320 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10320 = 2^{4} \times 3 \times 5 \times 43 \]10320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 32736 |
| Euler totient φ(n) | 2688 |
| Square | 106502400 |
| Cube | 1099104768000 |
| Square root | 101.587401 (= 4√645) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.032 × |
10320 in other forms
| Form | Value |
|---|---|
| In words | ten thousand three hundred and twenty |
| Binary (base 2) | 10100001010000 |
| Octal (base 8) | 24120 |
| Hexadecimal (base 16) | 2850 |
| Base 3 | 112011020 |
| As time | 10320 seconds = 2 h 52 min 0 s |
Is 10320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10320 ÷ 2 = 5160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10320 ÷ 3 = 3440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10320 ÷ 4 = 2580) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10320 ÷ 5 = 2064) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10320 ÷ 6 = 1720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (10320 ÷ 8 = 1290) | 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 (10320 ÷ 10 = 1032) | 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 (10320 ÷ 12 = 860) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10320 a prime number?
No. 10320 = × 3 × 5 × 43, so it is divisible by 2.
What are the factors of 10320?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160, 10320.
What is 10320 in binary?
10100001010000 (hexadecimal 2850, octal 24120).
What is the square root of 10320?
About 101.5874, exactly 4√645.
Is 10320 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10320?
10320 is a Harshad number: divisible by its digit sum 6.