The number 41688
41688 is a composite number with 32 divisors. Its prime factorisation is × × 193. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 193 … 41688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 41688: a Harshad number: divisible by its digit sum 27.
- 2
41688 is composite. Its prime factorisation is
- 3
The divisors add up to 116400; without 41688 itself that is 74712, so 41688 is abundant (74712 is more than 41688). Euler's totient φ(41688) = 13824 numbers up to 41688 share no factor with it.
- 4
The digits of 41688 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 41688 = 2^{3} \times 3^{3} \times 193 \]41688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 116400 |
| Euler totient φ(n) | 13824 |
| Square | 1737889344 |
| Cube | 72449130972672 |
| Square root | 204.176394 (= 6√1158) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 137 |
| Scientific notation | 4.1688 × |
41688 in other forms
| Form | Value |
|---|---|
| In words | forty-one thousand six hundred and eighty-eight |
| Binary (base 2) | 1010001011011000 |
| Octal (base 8) | 121330 |
| Hexadecimal (base 16) | A2D8 |
| Base 3 | 2010012000 |
| As time | 41688 seconds = 11 h 34 min 48 s |
Is 41688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (41688 ÷ 2 = 20844) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (41688 ÷ 3 = 13896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (41688 ÷ 4 = 10422) | 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 | Yes (41688 ÷ 6 = 6948) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (41688 ÷ 8 = 5211) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (41688 ÷ 9 = 4632) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (41688 ÷ 12 = 3474) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 41688 a prime number?
No. 41688 = × × 193, so it is divisible by 2.
What are the factors of 41688?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 193, 216, 386, 579, 772, 1158, 1544, 1737, 2316, 3474, 4632, 5211, 6948, 10422, 13896, 20844, 41688.
What is 41688 in binary?
1010001011011000 (hexadecimal A2D8, octal 121330).
What is the square root of 41688?
About 204.1764, exactly 6√1158.
Is 41688 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 41688?
41688 is a Harshad number: divisible by its digit sum 27.