The number 20160
20160 is a highly composite number: it has 84 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (84): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 20160.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20160: a highly composite number: it has 84 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
- 2
20160 is composite. Its prime factorisation is
- 3
The divisors add up to 79248; without 20160 itself that is 59088, so 20160 is abundant (59088 is more than 20160). Euler's totient φ(20160) = 4608 numbers up to 20160 share no factor with it.
- 4
The digits of 20160 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20160 = 2^{6} \times 3^{2} \times 5 \times 7 \]20160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 79248 |
| Euler totient φ(n) | 4608 |
| Square | 406425600 |
| Cube | 8193540096000 |
| Square root | 141.985915 (= 24√35) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.016 × |
20160 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand one hundred and sixty |
| Binary (base 2) | 100111011000000 |
| Octal (base 8) | 47300 |
| Hexadecimal (base 16) | 4EC0 |
| Base 3 | 1000122200 |
| As time | 20160 seconds = 5 h 36 min 0 s |
Is 20160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20160 ÷ 2 = 10080) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20160 ÷ 3 = 6720) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20160 ÷ 4 = 5040) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20160 ÷ 5 = 4032) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20160 ÷ 6 = 3360) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (20160 ÷ 7 = 2880) | 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 (20160 ÷ 8 = 2520) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (20160 ÷ 9 = 2240) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20160 ÷ 10 = 2016) | 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 (20160 ÷ 12 = 1680) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20160 a prime number?
No. 20160 = × × 5 × 7, so it is divisible by 2.
What are the factors of 20160?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080, 20160.
What is 20160 in binary?
100111011000000 (hexadecimal 4EC0, octal 47300).
What is the square root of 20160?
About 141.9859, exactly 24√35.
Is 20160 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 20160?
20160 is a highly composite number: it has 84 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.