The number 29984
29984 is a composite number with 12 divisors. Its prime factorisation is × 937. Divisors (12): 1, 2, 4, 8, 16, 32, 937, 1874, 3748, 7496, 14992, 29984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 29984: a Harshad number: divisible by its digit sum 32.
- 2
29984 is composite. Its prime factorisation is
- 3
The divisors add up to 59094; without 29984 itself that is 29110, so 29984 is deficient (29110 is less than 29984). Euler's totient φ(29984) = 14976 numbers up to 29984 share no factor with it.
- 4
The digits of 29984 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 178 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29984 = 2^{5} \times 937 \]29984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 59094 |
| Euler totient φ(n) | 14976 |
| Square | 899040256 |
| Cube | 26956823035904 |
| Square root | 173.158887 (= 4√1874) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 178 |
| Scientific notation | 2.9984 × |
29984 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand nine hundred and eighty-four |
| Binary (base 2) | 111010100100000 |
| Octal (base 8) | 72440 |
| Hexadecimal (base 16) | 7520 |
| Base 3 | 1112010112 |
| As time | 29984 seconds = 8 h 19 min 44 s |
Is 29984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29984 ÷ 2 = 14992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29984 ÷ 4 = 7496) | 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 | No (remainder 2) | 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 (29984 ÷ 8 = 3748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29984 a prime number?
No. 29984 = × 937, so it is divisible by 2.
What are the factors of 29984?
1, 2, 4, 8, 16, 32, 937, 1874, 3748, 7496, 14992, 29984.
What is 29984 in binary?
111010100100000 (hexadecimal 7520, octal 72440).
What is the square root of 29984?
About 173.1589, exactly 4√1874.
Is 29984 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 29984?
29984 is a Harshad number: divisible by its digit sum 32.