The number 688
688 is a composite number with 10 divisors. Its prime factorisation is × 43. Divisors (10): 1, 2, 4, 8, 16, 43, 86, 172, 344, 688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
688 is composite. Its prime factorisation is
- 3
The divisors add up to 1364; without 688 itself that is 676, so 688 is deficient (676 is less than 688). Euler's totient φ(688) = 336 numbers up to 688 share no factor with it.
- 4
The digits of 688 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 688 = 2^{4} \times 43 \]688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 1364 |
| Euler totient φ(n) | 336 |
| Square | 473344 |
| Cube | 325660672 |
| Square root | 26.229754 (= 4√43) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 33 |
| Scientific notation | 6.88 × |
688 in other forms
| Form | Value |
|---|---|
| In words | six hundred and eighty-eight |
| Roman numerals | DCLXXXVIII |
| Binary (base 2) | 1010110000 |
| Octal (base 8) | 1260 |
| Hexadecimal (base 16) | 2B0 |
| Base 3 | 221111 |
| As time | 688 seconds = 11 min 28 s |
Is 688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (688 ÷ 2 = 344) | 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 | Yes (688 ÷ 4 = 172) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (688 ÷ 8 = 86) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 688 a prime number?
No. 688 = × 43, so it is divisible by 2.
What are the factors of 688?
1, 2, 4, 8, 16, 43, 86, 172, 344, 688.
What is 688 in binary?
1010110000 (hexadecimal 2B0, octal 1260).
What is the square root of 688?
About 26.2298, exactly 4√43.
What is 688 in Roman numerals?
DCLXXXVIII.
Is 688 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 688?
It is a composite number with 10 divisors.