The number 27872
27872 is a palindrome: it reads 27872 backwards too. Its prime factorisation is × 13 × 67. Divisors (24): 1, 2, 4, 8, 13, 16, 26, 32, 52, 67, 104, 134, 208, 268, 416, 536 … 27872.
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How to work it out
- 1
What is special about 27872: a palindrome: it reads 27872 backwards too; a Harshad number: divisible by its digit sum 26.
- 2
27872 is composite. Its prime factorisation is
- 3
The divisors add up to 59976; without 27872 itself that is 32104, so 27872 is abundant (32104 is more than 27872). Euler's totient φ(27872) = 12672 numbers up to 27872 share no factor with it.
- 4
The digits of 27872 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 183 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27872 = 2^{5} \times 13 \times 67 \]27872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 59976 |
| Euler totient φ(n) | 12672 |
| Square | 776848384 |
| Cube | 21652318158848 |
| Square root | 166.949094 (= 4√1742) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 183 |
| Scientific notation | 2.7872 × |
27872 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 110110011100000 |
| Octal (base 8) | 66340 |
| Hexadecimal (base 16) | 6CE0 |
| Base 3 | 1102020022 |
| As time | 27872 seconds = 7 h 44 min 32 s |
Is 27872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27872 ÷ 2 = 13936) | 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 (27872 ÷ 4 = 6968) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 (27872 ÷ 8 = 3484) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27872 a prime number?
No. 27872 = × 13 × 67, so it is divisible by 2.
What are the factors of 27872?
1, 2, 4, 8, 13, 16, 26, 32, 52, 67, 104, 134, 208, 268, 416, 536, 871, 1072, 1742, 2144, 3484, 6968, 13936, 27872.
What is 27872 in binary?
110110011100000 (hexadecimal 6CE0, octal 66340).
What is the square root of 27872?
About 166.9491, exactly 4√1742.
Is 27872 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 27872?
27872 is a palindrome: it reads 27872 backwards too; a Harshad number: divisible by its digit sum 26.