The number 27180
27180 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 151. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 27180.
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How to work it out
- 1
What is special about 27180: a Harshad number: divisible by its digit sum 18.
- 2
27180 is composite. Its prime factorisation is
- 3
The divisors add up to 82992; without 27180 itself that is 55812, so 27180 is abundant (55812 is more than 27180). Euler's totient φ(27180) = 7200 numbers up to 27180 share no factor with it.
- 4
The digits of 27180 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27180 = 2^{2} \times 3^{2} \times 5 \times 151 \]27180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 82992 |
| Euler totient φ(n) | 7200 |
| Square | 738752400 |
| Cube | 20079290232000 |
| Square root | 164.863580 (= 6√755) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 2.718 × |
27180 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand one hundred and eighty |
| Binary (base 2) | 110101000101100 |
| Octal (base 8) | 65054 |
| Hexadecimal (base 16) | 6A2C |
| Base 3 | 1101021200 |
| As time | 27180 seconds = 7 h 33 min 0 s |
Is 27180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27180 ÷ 2 = 13590) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27180 ÷ 3 = 9060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27180 ÷ 4 = 6795) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27180 ÷ 5 = 5436) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27180 ÷ 6 = 4530) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27180 ÷ 9 = 3020) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27180 ÷ 10 = 2718) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27180 ÷ 12 = 2265) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27180 a prime number?
No. 27180 = × × 5 × 151, so it is divisible by 2.
What are the factors of 27180?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 151, 180, 302, 453, 604, 755, 906, 1359, 1510, 1812, 2265, 2718, 3020, 4530, 5436, 6795, 9060, 13590, 27180.
What is 27180 in binary?
110101000101100 (hexadecimal 6A2C, octal 65054).
What is the square root of 27180?
About 164.8636, exactly 6√755.
Is 27180 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27180?
27180 is a Harshad number: divisible by its digit sum 18.