The number 1721
1721 is a twin prime (1721 and 1723 are both prime) and the 268th prime number. Its only divisors are 1 and 1721.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1721: a twin prime (1721 and 1723 are both prime); the 268th prime number.
- 2
1721 is prime, so its only factors are 1 and 1721. It is the 268th prime; the next prime is 1723 and the one before is 1709.
- 3
The divisors add up to 1722; without 1721 itself that is 1, so 1721 is deficient (1 is less than 1721). Euler's totient φ(1721) = 1720 numbers up to 1721 share no factor with it.
- 4
The digits of 1721 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 55 steps to reach 1.
1721 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1722 |
| Euler totient φ(n) | 1720 |
| Square | 2961841 |
| Cube | 5097328361 |
| Square root | 41.484937 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 55 |
| Scientific notation | 1.721 × |
1721 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and twenty-one |
| Roman numerals | MDCCXXI |
| Binary (base 2) | 11010111001 |
| Octal (base 8) | 3271 |
| Hexadecimal (base 16) | 6B9 |
| Base 3 | 2100202 |
| As time | 1721 seconds = 28 min 41 s |
Is 1721 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 1) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | 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 1721 a prime number?
Yes. 1721 is divisible only by 1 and itself.
What are the factors of 1721?
1, 1721.
What is 1721 in binary?
11010111001 (hexadecimal 6B9, octal 3271).
What is the square root of 1721?
About 41.4849.
What is 1721 in Roman numerals?
MDCCXXI.
Is 1721 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 1721?
1721 is a twin prime (1721 and 1723 are both prime); the 268th prime number.