The number 27200
27200 is a composite number with 42 divisors. Its prime factorisation is × × 17. Divisors (42): 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68 … 27200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
27200 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27200 is composite. Its prime factorisation is
- 3
The divisors add up to 70866; without 27200 itself that is 43666, so 27200 is abundant (43666 is more than 27200). Euler's totient φ(27200) = 10240 numbers up to 27200 share no factor with it.
- 4
The digits of 27200 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27200 = 2^{6} \times 5^{2} \times 17 \]27200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 70866 |
| Euler totient φ(n) | 10240 |
| Square | 739840000 |
| Cube | 20123648000000 |
| Square root | 164.924225 (= 40√17) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 64 |
| Scientific notation | 2.72 × |
27200 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand two hundred |
| Binary (base 2) | 110101001000000 |
| Octal (base 8) | 65100 |
| Hexadecimal (base 16) | 6A40 |
| Base 3 | 1101022102 |
| As time | 27200 seconds = 7 h 33 min 20 s |
Is 27200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27200 ÷ 2 = 13600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27200 ÷ 4 = 6800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27200 ÷ 5 = 5440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (27200 ÷ 8 = 3400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27200 ÷ 10 = 2720) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27200 a prime number?
No. 27200 = × × 17, so it is divisible by 2.
What are the factors of 27200?
1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 680, 800, 850, 1088, 1360, 1600, 1700, 2720, 3400, 5440, 6800, 13600, 27200.
What is 27200 in binary?
110101001000000 (hexadecimal 6A40, octal 65100).
What is the square root of 27200?
About 164.9242, exactly 40√17.
Is 27200 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 27200?
It is a composite number with 42 divisors.