The number 41616
41616 is a perfect square (204²) and a triangular number: 1 + 2 + … + 288 = 41616. Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51 … 41616.
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How to work it out
- 1
What is special about 41616: a perfect square (204²); a triangular number: 1 + 2 + … + 288 = 41616; a Harshad number: divisible by its digit sum 18.
- 2
41616 is composite. Its prime factorisation is
- 3
The divisors add up to 123721; without 41616 itself that is 82105, so 41616 is abundant (82105 is more than 41616). Euler's totient φ(41616) = 13056 numbers up to 41616 share no factor with it.
- 4
The digits of 41616 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 181 steps to reach 1.
LaTeX source of the formulas on this page
\[ 41616 = 2^{4} \times 3^{2} \times 17^{2} \]41616 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 123721 |
| Euler totient φ(n) | 13056 |
| Square | 1731891456 |
| Cube | 72074394832896 |
| Square root | 204 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 181 |
| Scientific notation | 4.1616 × |
| Perfect power |
41616 in other forms
| Form | Value |
|---|---|
| In words | forty-one thousand six hundred and sixteen |
| Binary (base 2) | 1010001010010000 |
| Octal (base 8) | 121220 |
| Hexadecimal (base 16) | A290 |
| Base 3 | 2010002100 |
| As time | 41616 seconds = 11 h 33 min 36 s |
Is 41616 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (41616 ÷ 2 = 20808) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (41616 ÷ 3 = 13872) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (41616 ÷ 4 = 10404) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (41616 ÷ 6 = 6936) | 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 (41616 ÷ 8 = 5202) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (41616 ÷ 9 = 4624) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 | Yes (41616 ÷ 12 = 3468) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 41616 a prime number?
No. 41616 = × × , so it is divisible by 2.
What are the factors of 41616?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 289, 306, 408, 578, 612, 816, 867, 1156, 1224, 1734, 2312, 2448, 2601, 3468, 4624, 5202, 6936, 10404, 13872, 20808, 41616.
What is 41616 in binary?
1010001010010000 (hexadecimal A290, octal 121220).
What is the square root of 41616?
204, because 204 × 204 = 41616.
Is 41616 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 41616?
41616 is a perfect square (204²); a triangular number: 1 + 2 + … + 288 = 41616; a Harshad number: divisible by its digit sum 18.