The number 1321
1321 is a twin prime (1319 and 1321 are both prime) and the 216th prime number. Its only divisors are 1 and 1321.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1321: a twin prime (1319 and 1321 are both prime); the 216th prime number.
- 2
1321 is prime, so its only factors are 1 and 1321. It is the 216th prime; the next prime is 1327 and the one before is 1319.
- 3
The divisors add up to 1322; without 1321 itself that is 1, so 1321 is deficient (1 is less than 1321). Euler's totient φ(1321) = 1320 numbers up to 1321 share no factor with it.
- 4
The digits of 1321 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
1321 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1322 |
| Euler totient φ(n) | 1320 |
| Square | 1745041 |
| Cube | 2305199161 |
| Square root | 36.345564 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 101 |
| Scientific notation | 1.321 × |
1321 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and twenty-one |
| Roman numerals | MCCCXXI |
| Binary (base 2) | 10100101001 |
| Octal (base 8) | 2451 |
| Hexadecimal (base 16) | 529 |
| Base 3 | 1210221 |
| As time | 1321 seconds = 22 min 1 s |
Is 1321 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 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 1321 a prime number?
Yes. 1321 is divisible only by 1 and itself.
What are the factors of 1321?
1, 1321.
What is 1321 in binary?
10100101001 (hexadecimal 529, octal 2451).
What is the square root of 1321?
About 36.3456.
What is 1321 in Roman numerals?
MCCCXXI.
Is 1321 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1321?
1321 is a twin prime (1319 and 1321 are both prime); the 216th prime number.