The number 27120
27120 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 113. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 27120.
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How to work it out
- 1
What is special about 27120: a Harshad number: divisible by its digit sum 12.
- 2
27120 is composite. Its prime factorisation is
- 3
The divisors add up to 84816; without 27120 itself that is 57696, so 27120 is abundant (57696 is more than 27120). Euler's totient φ(27120) = 7168 numbers up to 27120 share no factor with it.
- 4
The digits of 27120 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 183 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27120 = 2^{4} \times 3 \times 5 \times 113 \]27120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 84816 |
| Euler totient φ(n) | 7168 |
| Square | 735494400 |
| Cube | 19946608128000 |
| Square root | 164.681511 (= 4√1695) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 183 |
| Scientific notation | 2.712 × |
27120 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand one hundred and twenty |
| Binary (base 2) | 110100111110000 |
| Octal (base 8) | 64760 |
| Hexadecimal (base 16) | 69F0 |
| Base 3 | 1101012110 |
| As time | 27120 seconds = 7 h 32 min 0 s |
Is 27120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27120 ÷ 2 = 13560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27120 ÷ 3 = 9040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27120 ÷ 4 = 6780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27120 ÷ 5 = 5424) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27120 ÷ 6 = 4520) | 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 (27120 ÷ 8 = 3390) | 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 (27120 ÷ 10 = 2712) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27120 ÷ 12 = 2260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27120 a prime number?
No. 27120 = × 3 × 5 × 113, so it is divisible by 2.
What are the factors of 27120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 113, 120, 226, 240, 339, 452, 565, 678, 904, 1130, 1356, 1695, 1808, 2260, 2712, 3390, 4520, 5424, 6780, 9040, 13560, 27120.
What is 27120 in binary?
110100111110000 (hexadecimal 69F0, octal 64760).
What is the square root of 27120?
About 164.6815, exactly 4√1695.
Is 27120 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 27120?
27120 is a Harshad number: divisible by its digit sum 12.