The number 41184
41184 is a composite number with 72 divisors. Its prime factorisation is × × 11 × 13. Divisors (72): 1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 22, 24, 26, 32 … 41184.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 41184: a Harshad number: divisible by its digit sum 18.
- 2
41184 is composite. Its prime factorisation is
- 3
The divisors add up to 137592; without 41184 itself that is 96408, so 41184 is abundant (96408 is more than 41184). Euler's totient φ(41184) = 11520 numbers up to 41184 share no factor with it.
- 4
The digits of 41184 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 150 steps to reach 1.
LaTeX source of the formulas on this page
\[ 41184 = 2^{5} \times 3^{2} \times 11 \times 13 \]41184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 137592 |
| Euler totient φ(n) | 11520 |
| Square | 1696121856 |
| Cube | 69853082517504 |
| Square root | 202.938414 (= 12√286) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 150 |
| Scientific notation | 4.1184 × |
41184 in other forms
| Form | Value |
|---|---|
| In words | forty-one thousand one hundred and eighty-four |
| Binary (base 2) | 1010000011100000 |
| Octal (base 8) | 120340 |
| Hexadecimal (base 16) | A0E0 |
| Base 3 | 2002111100 |
| As time | 41184 seconds = 11 h 26 min 24 s |
Is 41184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (41184 ÷ 2 = 20592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (41184 ÷ 3 = 13728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (41184 ÷ 4 = 10296) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (41184 ÷ 6 = 6864) | 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 (41184 ÷ 8 = 5148) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (41184 ÷ 9 = 4576) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (41184 ÷ 11 = 3744) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (41184 ÷ 12 = 3432) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 41184 a prime number?
No. 41184 = × × 11 × 13, so it is divisible by 2.
What are the factors of 41184?
1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 22, 24, 26, 32, 33, 36, 39, 44, 48, 52, 66, 72, 78, 88, 96, 99, 104, 117, 132, 143, 144, 156, 176, 198, 208, 234, 264, 286, 288, 312, 352, 396, 416, 429, 468, 528, 572, 624, 792, 858, 936, 1056, 1144, 1248, 1287, 1584, 1716, 1872, 2288, 2574, 3168, 3432, 3744, 4576, 5148, 6864, 10296, 13728, 20592, 41184.
What is 41184 in binary?
1010000011100000 (hexadecimal A0E0, octal 120340).
What is the square root of 41184?
About 202.9384, exactly 12√286.
Is 41184 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 41184?
41184 is a Harshad number: divisible by its digit sum 18.