The number 29988
29988 is a composite number with 54 divisors. Its prime factorisation is × × × 17. Divisors (54): 1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 28, 34, 36, 42 … 29988.
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How to work it out
- 1
What is special about 29988: a Harshad number: divisible by its digit sum 36.
- 2
29988 is composite. Its prime factorisation is
- 3
The divisors add up to 93366; without 29988 itself that is 63378, so 29988 is abundant (63378 is more than 29988). Euler's totient φ(29988) = 8064 numbers up to 29988 share no factor with it.
- 4
The digits of 29988 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29988 = 2^{2} \times 3^{2} \times 7^{2} \times 17 \]29988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 93366 |
| Euler totient φ(n) | 8064 |
| Square | 899280144 |
| Cube | 26967612958272 |
| Square root | 173.170436 (= 42√17) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 64 |
| Scientific notation | 2.9988 × |
29988 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand nine hundred and eighty-eight |
| Binary (base 2) | 111010100100100 |
| Octal (base 8) | 72444 |
| Hexadecimal (base 16) | 7524 |
| Base 3 | 1112010200 |
| As time | 29988 seconds = 8 h 19 min 48 s |
Is 29988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29988 ÷ 2 = 14994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29988 ÷ 3 = 9996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29988 ÷ 4 = 7497) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (29988 ÷ 6 = 4998) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (29988 ÷ 7 = 4284) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (29988 ÷ 9 = 3332) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (29988 ÷ 12 = 2499) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29988 a prime number?
No. 29988 = × × × 17, so it is divisible by 2.
What are the factors of 29988?
1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 28, 34, 36, 42, 49, 51, 63, 68, 84, 98, 102, 119, 126, 147, 153, 196, 204, 238, 252, 294, 306, 357, 441, 476, 588, 612, 714, 833, 882, 1071, 1428, 1666, 1764, 2142, 2499, 3332, 4284, 4998, 7497, 9996, 14994, 29988.
What is 29988 in binary?
111010100100100 (hexadecimal 7524, octal 72444).
What is the square root of 29988?
About 173.1704, exactly 42√17.
Is 29988 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 29988?
29988 is a Harshad number: divisible by its digit sum 36.