The number 693
693 is a binary palindrome (1010110101). Its prime factorisation is × 7 × 11. Divisors (12): 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 693: a binary palindrome (1010110101).
- 2
693 is composite. Its prime factorisation is
- 3
The divisors add up to 1248; without 693 itself that is 555, so 693 is deficient (555 is less than 693). Euler's totient φ(693) = 360 numbers up to 693 share no factor with it.
- 4
The digits of 693 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 693 = 3^{2} \times 7 \times 11 \]693 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1248 |
| Euler totient φ(n) | 360 |
| Square | 480249 |
| Cube | 332812557 |
| Square root | 26.324893 (= 3√77) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 33 |
| Scientific notation | 6.93 × |
693 in other forms
| Form | Value |
|---|---|
| In words | six hundred and ninety-three |
| Roman numerals | DCXCIII |
| Binary (base 2) | 1010110101 |
| Octal (base 8) | 1265 |
| Hexadecimal (base 16) | 2B5 |
| Base 3 | 221200 |
| As time | 693 seconds = 11 min 33 s |
Is 693 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 | Yes (693 ÷ 3 = 231) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (693 ÷ 7 = 99) | 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 | Yes (693 ÷ 9 = 77) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (693 ÷ 11 = 63) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 693 a prime number?
No. 693 = × 7 × 11, so it is divisible by 3.
What are the factors of 693?
1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
What is 693 in binary?
1010110101 (hexadecimal 2B5, octal 1265).
What is the square root of 693?
About 26.3249, exactly 3√77.
What is 693 in Roman numerals?
DCXCIII.
Is 693 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 693?
693 is a binary palindrome (1010110101).