The number 27456
27456 is a composite number with 56 divisors. Its prime factorisation is × 3 × 11 × 13. Divisors (56): 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 32, 33, 39 … 27456.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27456: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
27456 is composite. Its prime factorisation is
- 3
The divisors add up to 85344; without 27456 itself that is 57888, so 27456 is abundant (57888 is more than 27456). Euler's totient φ(27456) = 7680 numbers up to 27456 share no factor with it.
- 4
The digits of 27456 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27456 = 2^{6} \times 3 \times 11 \times 13 \]27456 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 85344 |
| Euler totient φ(n) | 7680 |
| Square | 753831936 |
| Cube | 20697209634816 |
| Square root | 165.698521 (= 8√429) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 108 |
| Scientific notation | 2.7456 × |
27456 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand four hundred and fifty-six |
| Binary (base 2) | 110101101000000 |
| Octal (base 8) | 65500 |
| Hexadecimal (base 16) | 6B40 |
| Base 3 | 1101122220 |
| As time | 27456 seconds = 7 h 37 min 36 s |
Is 27456 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27456 ÷ 2 = 13728) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27456 ÷ 3 = 9152) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27456 ÷ 4 = 6864) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27456 ÷ 6 = 4576) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (27456 ÷ 8 = 3432) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (27456 ÷ 11 = 2496) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27456 ÷ 12 = 2288) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27456 a prime number?
No. 27456 = × 3 × 11 × 13, so it is divisible by 2.
What are the factors of 27456?
1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 32, 33, 39, 44, 48, 52, 64, 66, 78, 88, 96, 104, 132, 143, 156, 176, 192, 208, 264, 286, 312, 352, 416, 429, 528, 572, 624, 704, 832, 858, 1056, 1144, 1248, 1716, 2112, 2288, 2496, 3432, 4576, 6864, 9152, 13728, 27456.
What is 27456 in binary?
110101101000000 (hexadecimal 6B40, octal 65500).
What is the square root of 27456?
About 165.6985, exactly 8√429.
Is 27456 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 27456?
27456 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.