The number 666
666 is a triangular number: 1 + 2 + … + 36 = 666 and a palindrome: it reads 666 backwards too. Its prime factorisation is 2 × × 37. Divisors (12): 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 666: a triangular number: 1 + 2 + … + 36 = 666; a palindrome: it reads 666 backwards too; a Harshad number: divisible by its digit sum 18.
- 2
666 is composite. Its prime factorisation is
- 3
The divisors add up to 1482; without 666 itself that is 816, so 666 is abundant (816 is more than 666). Euler's totient φ(666) = 216 numbers up to 666 share no factor with it.
- 4
The digits of 666 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 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 666 = 2 \times 3^{2} \times 37 \]666 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1482 |
| Euler totient φ(n) | 216 |
| Square | 443556 |
| Cube | 295408296 |
| Square root | 25.806976 (= 3√74) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 113 |
| Scientific notation | 6.66 × |
666 in other forms
| Form | Value |
|---|---|
| In words | six hundred and sixty-six |
| Roman numerals | DCLXVI |
| Binary (base 2) | 1010011010 |
| Octal (base 8) | 1232 |
| Hexadecimal (base 16) | 29A |
| Base 3 | 220200 |
| As time | 666 seconds = 11 min 6 s |
Is 666 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (666 ÷ 2 = 333) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (666 ÷ 3 = 222) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (666 ÷ 6 = 111) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (666 ÷ 9 = 74) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 666 a prime number?
No. 666 = 2 × × 37, so it is divisible by 2.
What are the factors of 666?
1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
What is 666 in binary?
1010011010 (hexadecimal 29A, octal 1232).
What is the square root of 666?
About 25.8070, exactly 3√74.
What is 666 in Roman numerals?
DCLXVI.
Is 666 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 666?
666 is a triangular number: 1 + 2 + … + 36 = 666; a palindrome: it reads 666 backwards too; a Harshad number: divisible by its digit sum 18.