The number 4104
4104 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 16³ and 9³ + 15³). Its prime factorisation is × × 19. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57 … 4104.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4104: a taxicab number: it is the sum of two cubes in 2 ways (2³ + 16³ and 9³ + 15³); a Harshad number: divisible by its digit sum 9.
- 2
4104 is composite. Its prime factorisation is
- 3
The divisors add up to 12000; without 4104 itself that is 7896, so 4104 is abundant (7896 is more than 4104). Euler's totient φ(4104) = 1296 numbers up to 4104 share no factor with it.
- 4
The digits of 4104 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4104 = 2^{3} \times 3^{3} \times 19 \]4104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 12000 |
| Euler totient φ(n) | 1296 |
| Square | 16842816 |
| Cube | 69122916864 |
| Square root | 64.062470 (= 6√114) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 4.104 × |
4104 in other forms
| Form | Value |
|---|---|
| In words | four thousand one hundred and four |
| Binary (base 2) | 1000000001000 |
| Octal (base 8) | 10010 |
| Hexadecimal (base 16) | 1008 |
| Base 3 | 12122000 |
| As time | 4104 seconds = 1 h 8 min 24 s |
Is 4104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4104 ÷ 2 = 2052) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4104 ÷ 3 = 1368) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4104 ÷ 4 = 1026) | 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 (4104 ÷ 6 = 684) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (4104 ÷ 8 = 513) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (4104 ÷ 9 = 456) | 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 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4104 ÷ 12 = 342) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4104 a prime number?
No. 4104 = × × 19, so it is divisible by 2.
What are the factors of 4104?
1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 108, 114, 152, 171, 216, 228, 342, 456, 513, 684, 1026, 1368, 2052, 4104.
What is 4104 in binary?
1000000001000 (hexadecimal 1008, octal 10010).
What is the square root of 4104?
About 64.0625, exactly 6√114.
Is 4104 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 4104?
4104 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 16³ and 9³ + 15³); a Harshad number: divisible by its digit sum 9.