The number 27048
27048 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 23. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 49 … 27048.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27048: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
27048 is composite. Its prime factorisation is
- 3
The divisors add up to 82080; without 27048 itself that is 55032, so 27048 is abundant (55032 is more than 27048). Euler's totient φ(27048) = 7392 numbers up to 27048 share no factor with it.
- 4
The digits of 27048 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27048 = 2^{3} \times 3 \times 7^{2} \times 23 \]27048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 82080 |
| Euler totient φ(n) | 7392 |
| Square | 731594304 |
| Cube | 19788162734592 |
| Square root | 164.462762 (= 14√138) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 46 |
| Scientific notation | 2.7048 × |
27048 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand and forty-eight |
| Binary (base 2) | 110100110101000 |
| Octal (base 8) | 64650 |
| Hexadecimal (base 16) | 69A8 |
| Base 3 | 1101002210 |
| As time | 27048 seconds = 7 h 30 min 48 s |
Is 27048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27048 ÷ 2 = 13524) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27048 ÷ 3 = 9016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27048 ÷ 4 = 6762) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27048 ÷ 6 = 4508) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27048 ÷ 7 = 3864) | 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 (27048 ÷ 8 = 3381) | 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 | No (remainder 8) | 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 (27048 ÷ 12 = 2254) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27048 a prime number?
No. 27048 = × 3 × × 23, so it is divisible by 2.
What are the factors of 27048?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 49, 56, 69, 84, 92, 98, 138, 147, 161, 168, 184, 196, 276, 294, 322, 392, 483, 552, 588, 644, 966, 1127, 1176, 1288, 1932, 2254, 3381, 3864, 4508, 6762, 9016, 13524, 27048.
What is 27048 in binary?
110100110101000 (hexadecimal 69A8, octal 64650).
What is the square root of 27048?
About 164.4628, exactly 14√138.
Is 27048 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27048?
27048 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.