The number 27216
27216 is a composite number with 60 divisors. Its prime factorisation is × × 7. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 27216.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27216: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
27216 is composite. Its prime factorisation is
- 3
The divisors add up to 90272; without 27216 itself that is 63056, so 27216 is abundant (63056 is more than 27216). Euler's totient φ(27216) = 7776 numbers up to 27216 share no factor with it.
- 4
The digits of 27216 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 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27216 = 2^{4} \times 3^{5} \times 7 \]27216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 90272 |
| Euler totient φ(n) | 7776 |
| Square | 740710656 |
| Cube | 20159181213696 |
| Square root | 164.972725 (= 36√21) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 64 |
| Scientific notation | 2.7216 × |
27216 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand two hundred and sixteen |
| Binary (base 2) | 110101001010000 |
| Octal (base 8) | 65120 |
| Hexadecimal (base 16) | 6A50 |
| Base 3 | 1101100000 |
| As time | 27216 seconds = 7 h 33 min 36 s |
Is 27216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27216 ÷ 2 = 13608) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27216 ÷ 3 = 9072) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27216 ÷ 4 = 6804) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27216 ÷ 6 = 4536) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27216 ÷ 7 = 3888) | 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 (27216 ÷ 8 = 3402) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27216 ÷ 9 = 3024) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27216 ÷ 12 = 2268) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27216 a prime number?
No. 27216 = × × 7, so it is divisible by 2.
What are the factors of 27216?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 756, 972, 1008, 1134, 1296, 1512, 1701, 1944, 2268, 3024, 3402, 3888, 4536, 6804, 9072, 13608, 27216.
What is 27216 in binary?
110101001010000 (hexadecimal 6A50, octal 65120).
What is the square root of 27216?
About 164.9727, exactly 36√21.
Is 27216 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27216?
27216 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.