The number 29904
29904 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 89. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56 … 29904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 29904: a Harshad number: divisible by its digit sum 24.
- 2
29904 is composite. Its prime factorisation is
- 3
The divisors add up to 89280; without 29904 itself that is 59376, so 29904 is abundant (59376 is more than 29904). Euler's totient φ(29904) = 8448 numbers up to 29904 share no factor with it.
- 4
The digits of 29904 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 90 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29904 = 2^{4} \times 3 \times 7 \times 89 \]29904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 89280 |
| Euler totient φ(n) | 8448 |
| Square | 894249216 |
| Cube | 26741628555264 |
| Square root | 172.927731 (= 4√1869) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 90 |
| Scientific notation | 2.9904 × |
29904 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand nine hundred and four |
| Binary (base 2) | 111010011010000 |
| Octal (base 8) | 72320 |
| Hexadecimal (base 16) | 74D0 |
| Base 3 | 1112000120 |
| As time | 29904 seconds = 8 h 18 min 24 s |
Is 29904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29904 ÷ 2 = 14952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29904 ÷ 3 = 9968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29904 ÷ 4 = 7476) | 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 (29904 ÷ 6 = 4984) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (29904 ÷ 7 = 4272) | 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 (29904 ÷ 8 = 3738) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (29904 ÷ 12 = 2492) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29904 a prime number?
No. 29904 = × 3 × 7 × 89, so it is divisible by 2.
What are the factors of 29904?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 89, 112, 168, 178, 267, 336, 356, 534, 623, 712, 1068, 1246, 1424, 1869, 2136, 2492, 3738, 4272, 4984, 7476, 9968, 14952, 29904.
What is 29904 in binary?
111010011010000 (hexadecimal 74D0, octal 72320).
What is the square root of 29904?
About 172.9277, exactly 4√1869.
Is 29904 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 29904?
29904 is a Harshad number: divisible by its digit sum 24.