The number 1307
1307 is the 214th prime number. Its only divisors are 1 and 1307.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1307: the 214th prime number.
- 2
1307 is prime, so its only factors are 1 and 1307. It is the 214th prime; the next prime is 1319 and the one before is 1303.
- 3
The divisors add up to 1308; without 1307 itself that is 1, so 1307 is deficient (1 is less than 1307). Euler's totient φ(1307) = 1306 numbers up to 1307 share no factor with it.
- 4
The digits of 1307 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 176 steps to reach 1.
1307 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1308 |
| Euler totient φ(n) | 1306 |
| Square | 1708249 |
| Cube | 2232681443 |
| Square root | 36.152455 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 176 |
| Scientific notation | 1.307 × |
1307 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and seven |
| Roman numerals | MCCCVII |
| Binary (base 2) | 10100011011 |
| Octal (base 8) | 2433 |
| Hexadecimal (base 16) | 51B |
| Base 3 | 1210102 |
| As time | 1307 seconds = 21 min 47 s |
Is 1307 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 2) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1307 a prime number?
Yes. 1307 is divisible only by 1 and itself.
What are the factors of 1307?
1, 1307.
What is 1307 in binary?
10100011011 (hexadecimal 51B, octal 2433).
What is the square root of 1307?
About 36.1525.
What is 1307 in Roman numerals?
MCCCVII.
Is 1307 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 1307?
1307 is the 214th prime number.