The number 27264
27264 is a composite number with 32 divisors. Its prime factorisation is × 3 × 71. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 128, 142 … 27264.
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How to work it out
- 1
What is special about 27264: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27264 is composite. Its prime factorisation is
- 3
The divisors add up to 73440; without 27264 itself that is 46176, so 27264 is abundant (46176 is more than 27264). Euler's totient φ(27264) = 8960 numbers up to 27264 share no factor with it.
- 4
The digits of 27264 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 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27264 = 2^{7} \times 3 \times 71 \]27264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 73440 |
| Euler totient φ(n) | 8960 |
| Square | 743325696 |
| Cube | 20266031775744 |
| Square root | 165.118140 (= 8√426) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 20 |
| Scientific notation | 2.7264 × |
27264 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand two hundred and sixty-four |
| Binary (base 2) | 110101010000000 |
| Octal (base 8) | 65200 |
| Hexadecimal (base 16) | 6A80 |
| Base 3 | 1101101210 |
| As time | 27264 seconds = 7 h 34 min 24 s |
Is 27264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27264 ÷ 2 = 13632) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27264 ÷ 3 = 9088) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27264 ÷ 4 = 6816) | 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 (27264 ÷ 6 = 4544) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (27264 ÷ 8 = 3408) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27264 ÷ 12 = 2272) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27264 a prime number?
No. 27264 = × 3 × 71, so it is divisible by 2.
What are the factors of 27264?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 128, 142, 192, 213, 284, 384, 426, 568, 852, 1136, 1704, 2272, 3408, 4544, 6816, 9088, 13632, 27264.
What is 27264 in binary?
110101010000000 (hexadecimal 6A80, octal 65200).
What is the square root of 27264?
About 165.1181, exactly 8√426.
Is 27264 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27264?
27264 is a happy number: repeatedly adding the squares of its digits reaches 1.