The number 27960
27960 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 233. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 27960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27960: a Harshad number: divisible by its digit sum 24.
- 2
27960 is composite. Its prime factorisation is
- 3
The divisors add up to 84240; without 27960 itself that is 56280, so 27960 is abundant (56280 is more than 27960). Euler's totient φ(27960) = 7424 numbers up to 27960 share no factor with it.
- 4
The digits of 27960 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27960 = 2^{3} \times 3 \times 5 \times 233 \]27960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 84240 |
| Euler totient φ(n) | 7424 |
| Square | 781761600 |
| Cube | 21858054336000 |
| Square root | 167.212440 (= 2√6990) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.796 × |
27960 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and sixty |
| Binary (base 2) | 110110100111000 |
| Octal (base 8) | 66470 |
| Hexadecimal (base 16) | 6D38 |
| Base 3 | 1102100120 |
| As time | 27960 seconds = 7 h 46 min 0 s |
Is 27960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27960 ÷ 2 = 13980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27960 ÷ 3 = 9320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27960 ÷ 4 = 6990) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27960 ÷ 5 = 5592) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27960 ÷ 6 = 4660) | 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 (27960 ÷ 8 = 3495) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27960 ÷ 10 = 2796) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27960 ÷ 12 = 2330) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27960 a prime number?
No. 27960 = × 3 × 5 × 233, so it is divisible by 2.
What are the factors of 27960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 233, 466, 699, 932, 1165, 1398, 1864, 2330, 2796, 3495, 4660, 5592, 6990, 9320, 13980, 27960.
What is 27960 in binary?
110110100111000 (hexadecimal 6D38, octal 66470).
What is the square root of 27960?
About 167.2124, exactly 2√6990.
Is 27960 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 27960?
27960 is a Harshad number: divisible by its digit sum 24.