The number 10920
10920 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 7 × 13. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 20, 21, 24 … 10920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10920: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
10920 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 10920 itself that is 29400, so 10920 is abundant (29400 is more than 10920). Euler's totient φ(10920) = 2304 numbers up to 10920 share no factor with it.
- 4
The digits of 10920 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 16 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10920 = 2^{3} \times 3 \times 5 \times 7 \times 13 \]10920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 2304 |
| Square | 119246400 |
| Cube | 1302170688000 |
| Square root | 104.498804 (= 2√2730) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 16 |
| Scientific notation | 1.092 × |
10920 in other forms
| Form | Value |
|---|---|
| In words | ten thousand nine hundred and twenty |
| Binary (base 2) | 10101010101000 |
| Octal (base 8) | 25250 |
| Hexadecimal (base 16) | 2AA8 |
| Base 3 | 112222110 |
| As time | 10920 seconds = 3 h 2 min 0 s |
Is 10920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10920 ÷ 2 = 5460) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10920 ÷ 3 = 3640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10920 ÷ 4 = 2730) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10920 ÷ 5 = 2184) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10920 ÷ 6 = 1820) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10920 ÷ 7 = 1560) | 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 (10920 ÷ 8 = 1365) | 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 (10920 ÷ 10 = 1092) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10920 ÷ 12 = 910) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10920 a prime number?
No. 10920 = × 3 × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 10920?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 20, 21, 24, 26, 28, 30, 35, 39, 40, 42, 52, 56, 60, 65, 70, 78, 84, 91, 104, 105, 120, 130, 140, 156, 168, 182, 195, 210, 260, 273, 280, 312, 364, 390, 420, 455, 520, 546, 728, 780, 840, 910, 1092, 1365, 1560, 1820, 2184, 2730, 3640, 5460, 10920.
What is 10920 in binary?
10101010101000 (hexadecimal 2AA8, octal 25250).
What is the square root of 10920?
About 104.4988, exactly 2√2730.
Is 10920 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10920?
10920 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.