The number 29184
29184 is a composite number with 40 divisors. Its prime factorisation is × 3 × 19. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76 … 29184.
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How to work it out
- 1
What is special about 29184: a Harshad number: divisible by its digit sum 24.
- 2
29184 is composite. Its prime factorisation is
- 3
The divisors add up to 81840; without 29184 itself that is 52656, so 29184 is abundant (52656 is more than 29184). Euler's totient φ(29184) = 9216 numbers up to 29184 share no factor with it.
- 4
The digits of 29184 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29184 = 2^{9} \times 3 \times 19 \]29184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 81840 |
| Euler totient φ(n) | 9216 |
| Square | 851705856 |
| Cube | 24856183701504 |
| Square root | 170.833252 (= 16√114) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 41 |
| Scientific notation | 2.9184 × |
29184 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand one hundred and eighty-four |
| Binary (base 2) | 111001000000000 |
| Octal (base 8) | 71000 |
| Hexadecimal (base 16) | 7200 |
| Base 3 | 1111000220 |
| As time | 29184 seconds = 8 h 6 min 24 s |
Is 29184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29184 ÷ 2 = 14592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29184 ÷ 3 = 9728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29184 ÷ 4 = 7296) | 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 (29184 ÷ 6 = 4864) | 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 (29184 ÷ 8 = 3648) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 (29184 ÷ 12 = 2432) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29184 a prime number?
No. 29184 = × 3 × 19, so it is divisible by 2.
What are the factors of 29184?
1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 128, 152, 192, 228, 256, 304, 384, 456, 512, 608, 768, 912, 1216, 1536, 1824, 2432, 3648, 4864, 7296, 9728, 14592, 29184.
What is 29184 in binary?
111001000000000 (hexadecimal 7200, octal 71000).
What is the square root of 29184?
About 170.8333, exactly 16√114.
Is 29184 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 29184?
29184 is a Harshad number: divisible by its digit sum 24.