The number 1681
1681 is a perfect square (41²). Its prime factorisation is . Divisors (3): 1, 41, 1681.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1681: a perfect square (41²); the square of a prime (41²).
- 2
1681 is composite. Its prime factorisation is
- 3
The divisors add up to 1723; without 1681 itself that is 42, so 1681 is deficient (42 is less than 1681). Euler's totient φ(1681) = 1640 numbers up to 1681 share no factor with it.
- 4
The digits of 1681 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1681 = 41^{2} \]1681 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 1723 |
| Euler totient φ(n) | 1640 |
| Square | 2825761 |
| Cube | 4750104241 |
| Square root | 41 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.681 × |
| Perfect power |
1681 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and eighty-one |
| Roman numerals | MDCLXXXI |
| Binary (base 2) | 11010010001 |
| Octal (base 8) | 3221 |
| Hexadecimal (base 16) | 691 |
| Base 3 | 2022021 |
| As time | 1681 seconds = 28 min 1 s |
Is 1681 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 1) | 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 9) | 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 1681 a prime number?
No. 1681 = , so it is divisible by 41.
What are the factors of 1681?
1, 41, 1681.
What is 1681 in binary?
11010010001 (hexadecimal 691, octal 3221).
What is the square root of 1681?
41, because 41 × 41 = 1681.
What is 1681 in Roman numerals?
MDCLXXXI.
Is 1681 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1681?
1681 is a perfect square (41²); the square of a prime (41²).