The number 1
1 is the unit: it is neither prime nor composite.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still the unit.
- 2
1 is neither prime nor composite.
- 3
The divisors add up to 1; without 1 itself that is 0, so 1 is neither abundant nor deficient. Euler's totient φ(1) = 1 numbers up to 1 share no factor with it.
- 4
The digits of 1 add up to 1, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 0 steps to reach 1.
1 at a glance
| Property | Value |
|---|---|
| Type | unit |
| Number of divisors | 1 |
| Sum of divisors | 1 |
| Euler totient φ(n) | 1 |
| Square | 1 |
| Cube | 1 |
| Square root | 1 |
| Digit sum / digital root | 1 / 1 |
| Collatz steps to 1 | 0 |
| Scientific notation | 1 × |
1 in other forms
| Form | Value |
|---|---|
| In words | one |
| Roman numerals | I |
| Binary (base 2) | 1 |
| Octal (base 8) | 1 |
| Hexadecimal (base 16) | 1 |
| Base 3 | 1 |
| As time | 1 seconds |
Is 1 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 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1 a prime number?
No. 1 is neither prime nor composite.
What are the factors of 1?
1.
What is 1 in binary?
1 (hexadecimal 1, octal 1).
What is the square root of 1?
1, because 1 × 1 = 1.
What is 1 in Roman numerals?
I.
Is 1 divisible by 3?
No. Its digits add up to 1, which is not a multiple of 3.
What is special about the number 1?
It is the unit with 1 divisors.