The number 29664
29664 is a composite number with 36 divisors. Its prime factorisation is × × 103. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 29664.
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How to work it out
- 1
29664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
29664 is composite. Its prime factorisation is
- 3
The divisors add up to 85176; without 29664 itself that is 55512, so 29664 is abundant (55512 is more than 29664). Euler's totient φ(29664) = 9792 numbers up to 29664 share no factor with it.
- 4
The digits of 29664 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 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29664 = 2^{5} \times 3^{2} \times 103 \]29664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 85176 |
| Euler totient φ(n) | 9792 |
| Square | 879952896 |
| Cube | 26102922706944 |
| Square root | 172.232401 (= 12√206) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.9664 × |
29664 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand six hundred and sixty-four |
| Binary (base 2) | 111001111100000 |
| Octal (base 8) | 71740 |
| Hexadecimal (base 16) | 73E0 |
| Base 3 | 1111200200 |
| As time | 29664 seconds = 8 h 14 min 24 s |
Is 29664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29664 ÷ 2 = 14832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29664 ÷ 3 = 9888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29664 ÷ 4 = 7416) | 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 (29664 ÷ 6 = 4944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (29664 ÷ 8 = 3708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (29664 ÷ 9 = 3296) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (29664 ÷ 12 = 2472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29664 a prime number?
No. 29664 = × × 103, so it is divisible by 2.
What are the factors of 29664?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 103, 144, 206, 288, 309, 412, 618, 824, 927, 1236, 1648, 1854, 2472, 3296, 3708, 4944, 7416, 9888, 14832, 29664.
What is 29664 in binary?
111001111100000 (hexadecimal 73E0, octal 71740).
What is the square root of 29664?
About 172.2324, exactly 12√206.
Is 29664 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 29664?
It is a composite number with 36 divisors.