The number 66
66 is a triangular number: 1 + 2 + … + 11 = 66 and a palindrome: it reads 66 backwards too. Its prime factorisation is 2 × 3 × 11. Divisors (8): 1, 2, 3, 6, 11, 22, 33, 66.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 66: a triangular number: 1 + 2 + … + 11 = 66; a palindrome: it reads 66 backwards too.
- 2
66 is composite. Its prime factorisation is
- 3
The divisors add up to 144; without 66 itself that is 78, so 66 is abundant (78 is more than 66). Euler's totient φ(66) = 20 numbers up to 66 share no factor with it.
- 4
The digits of 66 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 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 66 = 2 \times 3 \times 11 \]
66 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 144 |
| Euler totient φ(n) | 20 |
| Square | 4356 |
| Cube | 287496 |
| Square root | 8.124038 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 27 |
| Scientific notation | 6.6 × |
66 in other forms
| Form | Value |
|---|---|
| In words | sixty-six |
| Roman numerals | LXVI |
| Binary (base 2) | 1000010 |
| Octal (base 8) | 102 |
| Hexadecimal (base 16) | 42 |
| Base 3 | 2110 |
| As time | 66 seconds = 1 min 6 s |
Is 66 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (66 ÷ 2 = 33) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (66 ÷ 3 = 22) | 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 (66 ÷ 6 = 11) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 3) | 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 | Yes (66 ÷ 11 = 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 66 a prime number?
No. 66 = 2 × 3 × 11, so it is divisible by 2.
What are the factors of 66?
1, 2, 3, 6, 11, 22, 33, 66.
What is 66 in binary?
1000010 (hexadecimal 42, octal 102).
What is the square root of 66?
About 8.1240.
What is 66 in Roman numerals?
LXVI.
Is 66 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 66?
66 is a triangular number: 1 + 2 + … + 11 = 66; a palindrome: it reads 66 backwards too.