The number 1301
1301 is a twin prime (1301 and 1303 are both prime) and the 212th prime number. Its only divisors are 1 and 1301.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1301: a twin prime (1301 and 1303 are both prime); the 212th prime number.
- 2
1301 is prime, so its only factors are 1 and 1301. It is the 212th prime; the next prime is 1303 and the one before is 1297.
- 3
The divisors add up to 1302; without 1301 itself that is 1, so 1301 is deficient (1 is less than 1301). Euler's totient φ(1301) = 1300 numbers up to 1301 share no factor with it.
- 4
The digits of 1301 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
1301 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1302 |
| Euler totient φ(n) | 1300 |
| Square | 1692601 |
| Cube | 2202073901 |
| Square root | 36.069378 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.301 × |
1301 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and one |
| Roman numerals | MCCCI |
| Binary (base 2) | 10100010101 |
| Octal (base 8) | 2425 |
| Hexadecimal (base 16) | 515 |
| Base 3 | 1210012 |
| As time | 1301 seconds = 21 min 41 s |
Is 1301 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 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 5) | 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 5) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1301 a prime number?
Yes. 1301 is divisible only by 1 and itself.
What are the factors of 1301?
1, 1301.
What is 1301 in binary?
10100010101 (hexadecimal 515, octal 2425).
What is the square root of 1301?
About 36.0694.
What is 1301 in Roman numerals?
MCCCI.
Is 1301 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 1301?
1301 is a twin prime (1301 and 1303 are both prime); the 212th prime number.