The number 691
691 is the 125th prime number. Its only divisors are 1 and 691.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 691: the 125th prime number.
- 2
691 is prime, so its only factors are 1 and 691. It is the 125th prime; the next prime is 701 and the one before is 683.
- 3
The divisors add up to 692; without 691 itself that is 1, so 691 is deficient (1 is less than 691). Euler's totient φ(691) = 690 numbers up to 691 share no factor with it.
- 4
The digits of 691 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 126 steps to reach 1.
691 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 692 |
| Euler totient φ(n) | 690 |
| Square | 477481 |
| Cube | 329939371 |
| Square root | 26.286879 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 126 |
| Scientific notation | 6.91 × |
691 in other forms
| Form | Value |
|---|---|
| In words | six hundred and ninety-one |
| Roman numerals | DCXCI |
| Binary (base 2) | 1010110011 |
| Octal (base 8) | 1263 |
| Hexadecimal (base 16) | 2B3 |
| Base 3 | 221121 |
| As time | 691 seconds = 11 min 31 s |
Is 691 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 3) | 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 3) | 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 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 691 a prime number?
Yes. 691 is divisible only by 1 and itself.
What are the factors of 691?
1, 691.
What is 691 in binary?
1010110011 (hexadecimal 2B3, octal 1263).
What is the square root of 691?
About 26.2869.
What is 691 in Roman numerals?
DCXCI.
Is 691 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 691?
691 is the 125th prime number.