The number 3688
3688 is a composite number with 8 divisors. Its prime factorisation is × 461. Divisors (8): 1, 2, 4, 8, 461, 922, 1844, 3688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3688 is composite. Its prime factorisation is
- 3
The divisors add up to 6930; without 3688 itself that is 3242, so 3688 is deficient (3242 is less than 3688). Euler's totient φ(3688) = 1840 numbers up to 3688 share no factor with it.
- 4
The digits of 3688 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3688 = 2^{3} \times 461 \]3688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 6930 |
| Euler totient φ(n) | 1840 |
| Square | 13601344 |
| Cube | 50161756672 |
| Square root | 60.728906 (= 2√922) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.688 × |
3688 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred and eighty-eight |
| Roman numerals | MMMDCLXXXVIII |
| Binary (base 2) | 111001101000 |
| Octal (base 8) | 7150 |
| Hexadecimal (base 16) | E68 |
| Base 3 | 12001121 |
| As time | 3688 seconds = 1 h 1 min 28 s |
Is 3688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3688 ÷ 2 = 1844) | 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 (3688 ÷ 4 = 922) | 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 6) | 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 (3688 ÷ 8 = 461) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 3688 a prime number?
No. 3688 = × 461, so it is divisible by 2.
What are the factors of 3688?
1, 2, 4, 8, 461, 922, 1844, 3688.
What is 3688 in binary?
111001101000 (hexadecimal E68, octal 7150).
What is the square root of 3688?
About 60.7289, exactly 2√922.
What is 3688 in Roman numerals?
MMMDCLXXXVIII.
Is 3688 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 3688?
It is a composite number with 8 divisors.