The number 219
219 is a binary palindrome (11011011). Its prime factorisation is 3 × 73. Divisors (4): 1, 3, 73, 219.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 219: a binary palindrome (11011011); a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 3 × 73, the product of two primes.
- 2
219 is composite. Its prime factorisation is
- 3
The divisors add up to 296; without 219 itself that is 77, so 219 is deficient (77 is less than 219). Euler's totient φ(219) = 144 numbers up to 219 share no factor with it.
- 4
The digits of 219 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 219 = 3 \times 73 \]
219 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 296 |
| Euler totient φ(n) | 144 |
| Square | 47961 |
| Cube | 10503459 |
| Square root | 14.798649 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 2.19 × |
219 in other forms
| Form | Value |
|---|---|
| In words | two hundred and nineteen |
| Roman numerals | CCXIX |
| Binary (base 2) | 11011011 |
| Octal (base 8) | 333 |
| Hexadecimal (base 16) | DB |
| Base 3 | 22010 |
| As time | 219 seconds = 3 min 39 s |
Is 219 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (219 ÷ 3 = 73) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 219 a prime number?
No. 219 = 3 × 73, so it is divisible by 3.
What are the factors of 219?
1, 3, 73, 219.
What is 219 in binary?
11011011 (hexadecimal DB, octal 333).
What is the square root of 219?
About 14.7986.
What is 219 in Roman numerals?
CCXIX.
Is 219 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 219?
219 is a binary palindrome (11011011); a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 3 × 73, the product of two primes.