The number 27520
27520 is a composite number with 32 divisors. Its prime factorisation is × 5 × 43. Divisors (32): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 43, 64, 80, 86, 128, 160 … 27520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27520: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
27520 is composite. Its prime factorisation is
- 3
The divisors add up to 67320; without 27520 itself that is 39800, so 27520 is abundant (39800 is more than 27520). Euler's totient φ(27520) = 10752 numbers up to 27520 share no factor with it.
- 4
The digits of 27520 add up to 16, 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
\[ 27520 = 2^{7} \times 5 \times 43 \]27520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 67320 |
| Euler totient φ(n) | 10752 |
| Square | 757350400 |
| Cube | 20842283008000 |
| Square root | 165.891531 (= 8√430) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 108 |
| Scientific notation | 2.752 × |
27520 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand five hundred and twenty |
| Binary (base 2) | 110101110000000 |
| Octal (base 8) | 65600 |
| Hexadecimal (base 16) | 6B80 |
| Base 3 | 1101202021 |
| As time | 27520 seconds = 7 h 38 min 40 s |
Is 27520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27520 ÷ 2 = 13760) | 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 (27520 ÷ 4 = 6880) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27520 ÷ 5 = 5504) | 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 | No (remainder 3) | 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 (27520 ÷ 8 = 3440) | 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 | Yes (27520 ÷ 10 = 2752) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 27520 a prime number?
No. 27520 = × 5 × 43, so it is divisible by 2.
What are the factors of 27520?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 43, 64, 80, 86, 128, 160, 172, 215, 320, 344, 430, 640, 688, 860, 1376, 1720, 2752, 3440, 5504, 6880, 13760, 27520.
What is 27520 in binary?
110101110000000 (hexadecimal 6B80, octal 65600).
What is the square root of 27520?
About 165.8915, exactly 8√430.
Is 27520 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 27520?
27520 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.