The number 1080
1080 is a composite number with 32 divisors. Its prime factorisation is × × 5. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30 … 1080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1080: a Harshad number: divisible by its digit sum 9.
- 2
1080 is composite. Its prime factorisation is
- 3
The divisors add up to 3600; without 1080 itself that is 2520, so 1080 is abundant (2520 is more than 1080). Euler's totient φ(1080) = 288 numbers up to 1080 share no factor with it.
- 4
The digits of 1080 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1080 = 2^{3} \times 3^{3} \times 5 \]1080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 3600 |
| Euler totient φ(n) | 288 |
| Square | 1166400 |
| Cube | 1259712000 |
| Square root | 32.863353 (= 6√30) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.08 × |
1080 in other forms
| Form | Value |
|---|---|
| In words | one thousand and eighty |
| Roman numerals | MLXXX |
| Binary (base 2) | 10000111000 |
| Octal (base 8) | 2070 |
| Hexadecimal (base 16) | 438 |
| Base 3 | 1111000 |
| As time | 1080 seconds = 18 min 0 s |
Is 1080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1080 ÷ 2 = 540) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1080 ÷ 3 = 360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1080 ÷ 4 = 270) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1080 ÷ 5 = 216) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1080 ÷ 6 = 180) | 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 (1080 ÷ 8 = 135) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1080 ÷ 9 = 120) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1080 ÷ 10 = 108) | 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 (1080 ÷ 12 = 90) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1080 a prime number?
No. 1080 = × × 5, so it is divisible by 2.
What are the factors of 1080?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080.
What is 1080 in binary?
10000111000 (hexadecimal 438, octal 2070).
What is the square root of 1080?
About 32.8634, exactly 6√30.
What is 1080 in Roman numerals?
MLXXX.
Is 1080 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1080?
1080 is a Harshad number: divisible by its digit sum 9.