The number 3
3 is a Mersenne prime ( − 1), a triangular number: 1 + 2 + … + 2 = 3 and a twin prime (3 and 5 are both prime). Its only divisors are 1 and 3.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3: a Mersenne prime ( − 1); a triangular number: 1 + 2 + … + 2 = 3; a twin prime (3 and 5 are both prime); the 2nd prime number.
- 2
3 is prime, so its only factors are 1 and 3. It is the 2nd prime; the next prime is 5 and the one before is 2.
- 3
The divisors add up to 4; without 3 itself that is 1, so 3 is deficient (1 is less than 3). Euler's totient φ(3) = 2 numbers up to 3 share no factor with it.
- 4
The digits of 3 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 7 steps to reach 1.
3 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4 |
| Euler totient φ(n) | 2 |
| Square | 9 |
| Cube | 27 |
| Square root | 1.732051 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 7 |
| Scientific notation | 3 × |
3 in other forms
| Form | Value |
|---|---|
| In words | three |
| Roman numerals | III |
| Binary (base 2) | 11 |
| Octal (base 8) | 3 |
| Hexadecimal (base 16) | 3 |
| Base 3 | 10 |
| As time | 3 seconds |
Is 3 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 (3 ÷ 3 = 1) | 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 3) | 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 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 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 3 a prime number?
Yes. 3 is divisible only by 1 and itself.
What are the factors of 3?
1, 3.
What is 3 in binary?
11 (hexadecimal 3, octal 3).
What is the square root of 3?
About 1.7321.
What is 3 in Roman numerals?
III.
Is 3 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 3?
3 is a Mersenne prime ( − 1); a triangular number: 1 + 2 + … + 2 = 3; a twin prime (3 and 5 are both prime); the 2nd prime number.