The number 27480
27480 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 229. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 27480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27480: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27480 is composite. Its prime factorisation is
- 3
The divisors add up to 82800; without 27480 itself that is 55320, so 27480 is abundant (55320 is more than 27480). Euler's totient φ(27480) = 7296 numbers up to 27480 share no factor with it.
- 4
The digits of 27480 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 152 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27480 = 2^{3} \times 3 \times 5 \times 229 \]27480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 82800 |
| Euler totient φ(n) | 7296 |
| Square | 755150400 |
| Cube | 20751532992000 |
| Square root | 165.770926 (= 2√6870) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.748 × |
27480 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand four hundred and eighty |
| Binary (base 2) | 110101101011000 |
| Octal (base 8) | 65530 |
| Hexadecimal (base 16) | 6B58 |
| Base 3 | 1101200210 |
| As time | 27480 seconds = 7 h 38 min 0 s |
Is 27480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27480 ÷ 2 = 13740) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27480 ÷ 3 = 9160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27480 ÷ 4 = 6870) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27480 ÷ 5 = 5496) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27480 ÷ 6 = 4580) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (27480 ÷ 8 = 3435) | 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 (27480 ÷ 10 = 2748) | 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 (27480 ÷ 12 = 2290) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27480 a prime number?
No. 27480 = × 3 × 5 × 229, so it is divisible by 2.
What are the factors of 27480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 229, 458, 687, 916, 1145, 1374, 1832, 2290, 2748, 3435, 4580, 5496, 6870, 9160, 13740, 27480.
What is 27480 in binary?
110101101011000 (hexadecimal 6B58, octal 65530).
What is the square root of 27480?
About 165.7709, exactly 2√6870.
Is 27480 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27480?
27480 is a happy number: repeatedly adding the squares of its digits reaches 1.