The number 6
6 is a perfect number: its divisors below itself add up to 6, a highly composite number: it has 4 divisors, more than any smaller number and 3! (3 factorial). Its prime factorisation is 2 × 3. Divisors (4): 1, 2, 3, 6.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6: a perfect number: its divisors below itself add up to 6; a highly composite number: it has 4 divisors, more than any smaller number; 3! (3 factorial); a triangular number: 1 + 2 + … + 3 = 6; a semiprime: 2 × 3, the product of two primes.
- 2
6 is composite. Its prime factorisation is
- 3
The divisors add up to 12; without 6 itself that is 6, so 6 is a perfect number. Euler's totient φ(6) = 2 numbers up to 6 share no factor with it.
- 4
The digits of 6 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 8 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6 = 2 \times 3 \]
6 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 12 |
| Euler totient φ(n) | 2 |
| Square | 36 |
| Cube | 216 |
| Square root | 2.449490 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 8 |
| Scientific notation | 6 × |
6 in other forms
| Form | Value |
|---|---|
| In words | six |
| Roman numerals | VI |
| Binary (base 2) | 110 |
| Octal (base 8) | 6 |
| Hexadecimal (base 16) | 6 |
| Base 3 | 20 |
| As time | 6 seconds |
Is 6 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6 ÷ 2 = 3) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6 ÷ 3 = 2) | 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 (6 ÷ 6 = 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6 a prime number?
No. 6 = 2 × 3, so it is divisible by 2.
What are the factors of 6?
1, 2, 3, 6.
What is 6 in binary?
110 (hexadecimal 6, octal 6).
What is the square root of 6?
About 2.4495.
What is 6 in Roman numerals?
VI.
Is 6 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 6?
6 is a perfect number: its divisors below itself add up to 6; a highly composite number: it has 4 divisors, more than any smaller number; 3! (3 factorial); a triangular number: 1 + 2 + … + 3 = 6; a semiprime: 2 × 3, the product of two primes.