The number 27664
27664 is a composite number with 40 divisors. Its prime factorisation is × 7 × 13 × 19. Divisors (40): 1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 38, 52, 56, 76, 91 … 27664.
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How to work it out
- 1
27664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27664 is composite. Its prime factorisation is
- 3
The divisors add up to 69440; without 27664 itself that is 41776, so 27664 is abundant (41776 is more than 27664). Euler's totient φ(27664) = 10368 numbers up to 27664 share no factor with it.
- 4
The digits of 27664 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27664 = 2^{4} \times 7 \times 13 \times 19 \]27664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 69440 |
| Euler totient φ(n) | 10368 |
| Square | 765296896 |
| Cube | 21171173330944 |
| Square root | 166.324983 (= 4√1729) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 108 |
| Scientific notation | 2.7664 × |
27664 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand six hundred and sixty-four |
| Binary (base 2) | 110110000010000 |
| Octal (base 8) | 66020 |
| Hexadecimal (base 16) | 6C10 |
| Base 3 | 1101221121 |
| As time | 27664 seconds = 7 h 41 min 4 s |
Is 27664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27664 ÷ 2 = 13832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27664 ÷ 4 = 6916) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27664 ÷ 7 = 3952) | 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 (27664 ÷ 8 = 3458) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27664 a prime number?
No. 27664 = × 7 × 13 × 19, so it is divisible by 2.
What are the factors of 27664?
1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 38, 52, 56, 76, 91, 104, 112, 133, 152, 182, 208, 247, 266, 304, 364, 494, 532, 728, 988, 1064, 1456, 1729, 1976, 2128, 3458, 3952, 6916, 13832, 27664.
What is 27664 in binary?
110110000010000 (hexadecimal 6C10, octal 66020).
What is the square root of 27664?
About 166.3250, exactly 4√1729.
Is 27664 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 27664?
It is a composite number with 40 divisors.