The number 29760
29760 is a composite number with 56 divisors. Its prime factorisation is × 3 × 5 × 31. Divisors (56): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32 … 29760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 29760: a Harshad number: divisible by its digit sum 24.
- 2
29760 is composite. Its prime factorisation is
- 3
The divisors add up to 97536; without 29760 itself that is 67776, so 29760 is abundant (67776 is more than 29760). Euler's totient φ(29760) = 7680 numbers up to 29760 share no factor with it.
- 4
The digits of 29760 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29760 = 2^{6} \times 3 \times 5 \times 31 \]29760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 97536 |
| Euler totient φ(n) | 7680 |
| Square | 885657600 |
| Cube | 26357170176000 |
| Square root | 172.510869 (= 8√465) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 41 |
| Scientific notation | 2.976 × |
29760 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand seven hundred and sixty |
| Binary (base 2) | 111010001000000 |
| Octal (base 8) | 72100 |
| Hexadecimal (base 16) | 7440 |
| Base 3 | 1111211020 |
| As time | 29760 seconds = 8 h 16 min 0 s |
Is 29760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29760 ÷ 2 = 14880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29760 ÷ 3 = 9920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (29760 ÷ 4 = 7440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (29760 ÷ 5 = 5952) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (29760 ÷ 6 = 4960) | 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 (29760 ÷ 8 = 3720) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (29760 ÷ 10 = 2976) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (29760 ÷ 12 = 2480) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29760 a prime number?
No. 29760 = × 3 × 5 × 31, so it is divisible by 2.
What are the factors of 29760?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 155, 160, 186, 192, 240, 248, 310, 320, 372, 465, 480, 496, 620, 744, 930, 960, 992, 1240, 1488, 1860, 1984, 2480, 2976, 3720, 4960, 5952, 7440, 9920, 14880, 29760.
What is 29760 in binary?
111010001000000 (hexadecimal 7440, octal 72100).
What is the square root of 29760?
About 172.5109, exactly 8√465.
Is 29760 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 29760?
29760 is a Harshad number: divisible by its digit sum 24.