The number 29952
29952 is a composite number with 54 divisors. Its prime factorisation is × × 13. Divisors (54): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 29952.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
29952 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
29952 is composite. Its prime factorisation is
- 3
The divisors add up to 93002; without 29952 itself that is 63050, so 29952 is abundant (63050 is more than 29952). Euler's totient φ(29952) = 9216 numbers up to 29952 share no factor with it.
- 4
The digits of 29952 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29952 = 2^{8} \times 3^{2} \times 13 \]29952 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 93002 |
| Euler totient φ(n) | 9216 |
| Square | 897122304 |
| Cube | 26870607249408 |
| Square root | 173.066461 (= 48√13) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 28 |
| Scientific notation | 2.9952 × |
29952 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand nine hundred and fifty-two |
| Binary (base 2) | 111010100000000 |
| Octal (base 8) | 72400 |
| Hexadecimal (base 16) | 7500 |
| Base 3 | 1112002100 |
| As time | 29952 seconds = 8 h 19 min 12 s |
Is 29952 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29952 ÷ 2 = 14976) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29952 ÷ 3 = 9984) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29952 ÷ 4 = 7488) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (29952 ÷ 6 = 4992) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (29952 ÷ 8 = 3744) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (29952 ÷ 9 = 3328) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (29952 ÷ 12 = 2496) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29952 a prime number?
No. 29952 = × × 13, so it is divisible by 2.
What are the factors of 29952?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 128, 144, 156, 192, 208, 234, 256, 288, 312, 384, 416, 468, 576, 624, 768, 832, 936, 1152, 1248, 1664, 1872, 2304, 2496, 3328, 3744, 4992, 7488, 9984, 14976, 29952.
What is 29952 in binary?
111010100000000 (hexadecimal 7500, octal 72400).
What is the square root of 29952?
About 173.0665, exactly 48√13.
Is 29952 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 29952?
It is a composite number with 54 divisors.