The number 27504
27504 is a composite number with 30 divisors. Its prime factorisation is × × 191. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 191 … 27504.
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How to work it out
- 1
What is special about 27504: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
27504 is composite. Its prime factorisation is
- 3
The divisors add up to 77376; without 27504 itself that is 49872, so 27504 is abundant (49872 is more than 27504). Euler's totient φ(27504) = 9120 numbers up to 27504 share no factor with it.
- 4
The digits of 27504 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 152 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27504 = 2^{4} \times 3^{2} \times 191 \]27504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 77376 |
| Euler totient φ(n) | 9120 |
| Square | 756470016 |
| Cube | 20805951320064 |
| Square root | 165.843300 (= 12√191) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.7504 × |
27504 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand five hundred and four |
| Binary (base 2) | 110101101110000 |
| Octal (base 8) | 65560 |
| Hexadecimal (base 16) | 6B70 |
| Base 3 | 1101201200 |
| As time | 27504 seconds = 7 h 38 min 24 s |
Is 27504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27504 ÷ 2 = 13752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27504 ÷ 3 = 9168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27504 ÷ 4 = 6876) | 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 (27504 ÷ 6 = 4584) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (27504 ÷ 8 = 3438) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27504 ÷ 9 = 3056) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27504 ÷ 12 = 2292) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27504 a prime number?
No. 27504 = × × 191, so it is divisible by 2.
What are the factors of 27504?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 191, 382, 573, 764, 1146, 1528, 1719, 2292, 3056, 3438, 4584, 6876, 9168, 13752, 27504.
What is 27504 in binary?
110101101110000 (hexadecimal 6B70, octal 65560).
What is the square root of 27504?
About 165.8433, exactly 12√191.
Is 27504 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27504?
27504 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.