The number 1688
1688 is a composite number with 8 divisors. Its prime factorisation is × 211. Divisors (8): 1, 2, 4, 8, 211, 422, 844, 1688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1688 is composite. Its prime factorisation is
- 3
The divisors add up to 3180; without 1688 itself that is 1492, so 1688 is deficient (1492 is less than 1688). Euler's totient φ(1688) = 840 numbers up to 1688 share no factor with it.
- 4
The digits of 1688 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1688 = 2^{3} \times 211 \]1688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3180 |
| Euler totient φ(n) | 840 |
| Square | 2849344 |
| Cube | 4809692672 |
| Square root | 41.085277 (= 2√422) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.688 × |
1688 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and eighty-eight |
| Roman numerals | MDCLXXXVIII |
| Binary (base 2) | 11010011000 |
| Octal (base 8) | 3230 |
| Hexadecimal (base 16) | 698 |
| Base 3 | 2022112 |
| As time | 1688 seconds = 28 min 8 s |
Is 1688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1688 ÷ 2 = 844) | 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 | Yes (1688 ÷ 4 = 422) | 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 2) | 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 | Yes (1688 ÷ 8 = 211) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1688 a prime number?
No. 1688 = × 211, so it is divisible by 2.
What are the factors of 1688?
1, 2, 4, 8, 211, 422, 844, 1688.
What is 1688 in binary?
11010011000 (hexadecimal 698, octal 3230).
What is the square root of 1688?
About 41.0853, exactly 2√422.
What is 1688 in Roman numerals?
MDCLXXXVIII.
Is 1688 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 1688?
It is a composite number with 8 divisors.