The number 27144
27144 is a composite number with 48 divisors. Its prime factorisation is × × 13 × 29. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 29, 36, 39, 52 … 27144.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27144: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
27144 is composite. Its prime factorisation is
- 3
The divisors add up to 81900; without 27144 itself that is 54756, so 27144 is abundant (54756 is more than 27144). Euler's totient φ(27144) = 8064 numbers up to 27144 share no factor with it.
- 4
The digits of 27144 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27144 = 2^{3} \times 3^{2} \times 13 \times 29 \]27144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 81900 |
| Euler totient φ(n) | 8064 |
| Square | 736796736 |
| Cube | 19999610601984 |
| Square root | 164.754363 (= 6√754) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 46 |
| Scientific notation | 2.7144 × |
27144 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand one hundred and forty-four |
| Binary (base 2) | 110101000001000 |
| Octal (base 8) | 65010 |
| Hexadecimal (base 16) | 6A08 |
| Base 3 | 1101020100 |
| As time | 27144 seconds = 7 h 32 min 24 s |
Is 27144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27144 ÷ 2 = 13572) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27144 ÷ 3 = 9048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27144 ÷ 4 = 6786) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27144 ÷ 6 = 4524) | 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 (27144 ÷ 8 = 3393) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27144 ÷ 9 = 3016) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27144 ÷ 12 = 2262) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27144 a prime number?
No. 27144 = × × 13 × 29, so it is divisible by 2.
What are the factors of 27144?
1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 29, 36, 39, 52, 58, 72, 78, 87, 104, 116, 117, 156, 174, 232, 234, 261, 312, 348, 377, 468, 522, 696, 754, 936, 1044, 1131, 1508, 2088, 2262, 3016, 3393, 4524, 6786, 9048, 13572, 27144.
What is 27144 in binary?
110101000001000 (hexadecimal 6A08, octal 65010).
What is the square root of 27144?
About 164.7544, exactly 6√754.
Is 27144 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27144?
27144 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.