The number 2160
2160 is a composite number with 40 divisors. Its prime factorisation is × × 5. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 2160.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2160: a Harshad number: divisible by its digit sum 9.
- 2
2160 is composite. Its prime factorisation is
- 3
The divisors add up to 7440; without 2160 itself that is 5280, so 2160 is abundant (5280 is more than 2160). Euler's totient φ(2160) = 576 numbers up to 2160 share no factor with it.
- 4
The digits of 2160 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2160 = 2^{4} \times 3^{3} \times 5 \]2160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 7440 |
| Euler totient φ(n) | 576 |
| Square | 4665600 |
| Cube | 10077696000 |
| Square root | 46.475800 (= 12√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 45 |
| Scientific notation | 2.16 × |
2160 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and sixty |
| Roman numerals | MMCLX |
| Binary (base 2) | 100001110000 |
| Octal (base 8) | 4160 |
| Hexadecimal (base 16) | 870 |
| Base 3 | 2222000 |
| As time | 2160 seconds = 36 min 0 s |
Is 2160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2160 ÷ 2 = 1080) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2160 ÷ 3 = 720) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2160 ÷ 4 = 540) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2160 ÷ 5 = 432) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2160 ÷ 6 = 360) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (2160 ÷ 8 = 270) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2160 ÷ 9 = 240) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2160 ÷ 10 = 216) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2160 ÷ 12 = 180) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2160 a prime number?
No. 2160 = × × 5, so it is divisible by 2.
What are the factors of 2160?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160.
What is 2160 in binary?
100001110000 (hexadecimal 870, octal 4160).
What is the square root of 2160?
About 46.4758, exactly 12√15.
What is 2160 in Roman numerals?
MMCLX.
Is 2160 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2160?
2160 is a Harshad number: divisible by its digit sum 9.