The number 13
13 is a Fibonacci number, a twin prime (11 and 13 are both prime) and the 6th prime number. Its only divisors are 1 and 13.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13: a Fibonacci number; a twin prime (11 and 13 are both prime); the 6th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13 is prime, so its only factors are 1 and 13. It is the 6th prime; the next prime is 17 and the one before is 11.
- 3
The divisors add up to 14; without 13 itself that is 1, so 13 is deficient (1 is less than 13). Euler's totient φ(13) = 12 numbers up to 13 share no factor with it.
- 4
The digits of 13 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 9 steps to reach 1.
13 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 14 |
| Euler totient φ(n) | 12 |
| Square | 169 |
| Cube | 2197 |
| Square root | 3.605551 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 9 |
| Scientific notation | 1.3 × |
13 in other forms
| Form | Value |
|---|---|
| In words | thirteen |
| Roman numerals | XIII |
| Binary (base 2) | 1101 |
| Octal (base 8) | 15 |
| Hexadecimal (base 16) | D |
| Base 3 | 111 |
| As time | 13 seconds |
Is 13 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 3) | 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 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 2) | 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 13 a prime number?
Yes. 13 is divisible only by 1 and itself.
What are the factors of 13?
1, 13.
What is 13 in binary?
1101 (hexadecimal D, octal 15).
What is the square root of 13?
About 3.6056.
What is 13 in Roman numerals?
XIII.
Is 13 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 13?
13 is a Fibonacci number; a twin prime (11 and 13 are both prime); the 6th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.