The number 27528
27528 is a composite number with 32 divisors. Its prime factorisation is × 3 × 31 × 37. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 24, 31, 37, 62, 74, 93, 111, 124, 148 … 27528.
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How to work it out
- 1
What is special about 27528: a Harshad number: divisible by its digit sum 24.
- 2
27528 is composite. Its prime factorisation is
- 3
The divisors add up to 72960; without 27528 itself that is 45432, so 27528 is abundant (45432 is more than 27528). Euler's totient φ(27528) = 8640 numbers up to 27528 share no factor with it.
- 4
The digits of 27528 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
\[ 27528 = 2^{3} \times 3 \times 31 \times 37 \]27528 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 72960 |
| Euler totient φ(n) | 8640 |
| Square | 757790784 |
| Cube | 20860464701952 |
| Square root | 165.915641 (= 2√6882) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 108 |
| Scientific notation | 2.7528 × |
27528 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand five hundred and twenty-eight |
| Binary (base 2) | 110101110001000 |
| Octal (base 8) | 65610 |
| Hexadecimal (base 16) | 6B88 |
| Base 3 | 1101202120 |
| As time | 27528 seconds = 7 h 38 min 48 s |
Is 27528 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27528 ÷ 2 = 13764) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27528 ÷ 3 = 9176) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27528 ÷ 4 = 6882) | 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 (27528 ÷ 6 = 4588) | 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 | Yes (27528 ÷ 8 = 3441) | 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 8) | 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 (27528 ÷ 12 = 2294) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27528 a prime number?
No. 27528 = × 3 × 31 × 37, so it is divisible by 2.
What are the factors of 27528?
1, 2, 3, 4, 6, 8, 12, 24, 31, 37, 62, 74, 93, 111, 124, 148, 186, 222, 248, 296, 372, 444, 744, 888, 1147, 2294, 3441, 4588, 6882, 9176, 13764, 27528.
What is 27528 in binary?
110101110001000 (hexadecimal 6B88, octal 65610).
What is the square root of 27528?
About 165.9156, exactly 2√6882.
Is 27528 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 27528?
27528 is a Harshad number: divisible by its digit sum 24.