The number 27738
27738 is a composite number with 24 divisors. Its prime factorisation is 2 × × 23 × 67. Divisors (24): 1, 2, 3, 6, 9, 18, 23, 46, 67, 69, 134, 138, 201, 207, 402, 414 … 27738.
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How to work it out
- 1
27738 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27738 is composite. Its prime factorisation is
- 3
The divisors add up to 63648; without 27738 itself that is 35910, so 27738 is abundant (35910 is more than 27738). Euler's totient φ(27738) = 8712 numbers up to 27738 share no factor with it.
- 4
The digits of 27738 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 152 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27738 = 2 \times 3^{2} \times 23 \times 67 \]27738 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 63648 |
| Euler totient φ(n) | 8712 |
| Square | 769396644 |
| Cube | 21341524111272 |
| Square root | 166.547291 (= 3√3082) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.7738 × |
27738 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand seven hundred and thirty-eight |
| Binary (base 2) | 110110001011010 |
| Octal (base 8) | 66132 |
| Hexadecimal (base 16) | 6C5A |
| Base 3 | 1102001100 |
| As time | 27738 seconds = 7 h 42 min 18 s |
Is 27738 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27738 ÷ 2 = 13869) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27738 ÷ 3 = 9246) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (27738 ÷ 6 = 4623) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27738 ÷ 9 = 3082) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27738 a prime number?
No. 27738 = 2 × × 23 × 67, so it is divisible by 2.
What are the factors of 27738?
1, 2, 3, 6, 9, 18, 23, 46, 67, 69, 134, 138, 201, 207, 402, 414, 603, 1206, 1541, 3082, 4623, 9246, 13869, 27738.
What is 27738 in binary?
110110001011010 (hexadecimal 6C5A, octal 66132).
What is the square root of 27738?
About 166.5473, exactly 3√3082.
Is 27738 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 27738?
It is a composite number with 24 divisors.