The number 29646
29646 is a triangular number: 1 + 2 + … + 243 = 29646. Its prime factorisation is 2 × × 61. Divisors (24): 1, 2, 3, 6, 9, 18, 27, 54, 61, 81, 122, 162, 183, 243, 366, 486 … 29646.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 29646: a triangular number: 1 + 2 + … + 243 = 29646; a Harshad number: divisible by its digit sum 27.
- 2
29646 is composite. Its prime factorisation is
- 3
The divisors add up to 67704; without 29646 itself that is 38058, so 29646 is abundant (38058 is more than 29646). Euler's totient φ(29646) = 9720 numbers up to 29646 share no factor with it.
- 4
The digits of 29646 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
\[ 29646 = 2 \times 3^{5} \times 61 \]29646 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 67704 |
| Euler totient φ(n) | 9720 |
| Square | 878885316 |
| Cube | 26055434078136 |
| Square root | 172.180138 (= 9√366) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.9646 × |
29646 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand six hundred and forty-six |
| Binary (base 2) | 111001111001110 |
| Octal (base 8) | 71716 |
| Hexadecimal (base 16) | 73CE |
| Base 3 | 1111200000 |
| As time | 29646 seconds = 8 h 14 min 6 s |
Is 29646 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29646 ÷ 2 = 14823) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29646 ÷ 3 = 9882) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (29646 ÷ 6 = 4941) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (29646 ÷ 9 = 3294) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29646 a prime number?
No. 29646 = 2 × × 61, so it is divisible by 2.
What are the factors of 29646?
1, 2, 3, 6, 9, 18, 27, 54, 61, 81, 122, 162, 183, 243, 366, 486, 549, 1098, 1647, 3294, 4941, 9882, 14823, 29646.
What is 29646 in binary?
111001111001110 (hexadecimal 73CE, octal 71716).
What is the square root of 29646?
About 172.1801, exactly 9√366.
Is 29646 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 29646?
29646 is a triangular number: 1 + 2 + … + 243 = 29646; a Harshad number: divisible by its digit sum 27.