The number 35760
35760 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 149. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 35760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
35760 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
35760 is composite. Its prime factorisation is
- 3
The divisors add up to 111600; without 35760 itself that is 75840, so 35760 is abundant (75840 is more than 35760). Euler's totient φ(35760) = 9472 numbers up to 35760 share no factor with it.
- 4
The digits of 35760 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 35760 = 2^{4} \times 3 \times 5 \times 149 \]35760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 111600 |
| Euler totient φ(n) | 9472 |
| Square | 1278777600 |
| Cube | 45729086976000 |
| Square root | 189.103146 (= 4√2235) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.576 × |
35760 in other forms
| Form | Value |
|---|---|
| In words | thirty-five thousand seven hundred and sixty |
| Binary (base 2) | 1000101110110000 |
| Octal (base 8) | 105660 |
| Hexadecimal (base 16) | 8BB0 |
| Base 3 | 1211001110 |
| As time | 35760 seconds = 9 h 56 min 0 s |
Is 35760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (35760 ÷ 2 = 17880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (35760 ÷ 3 = 11920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (35760 ÷ 4 = 8940) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (35760 ÷ 5 = 7152) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (35760 ÷ 6 = 5960) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (35760 ÷ 8 = 4470) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (35760 ÷ 10 = 3576) | 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 (35760 ÷ 12 = 2980) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 35760 a prime number?
No. 35760 = × 3 × 5 × 149, so it is divisible by 2.
What are the factors of 35760?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 149, 240, 298, 447, 596, 745, 894, 1192, 1490, 1788, 2235, 2384, 2980, 3576, 4470, 5960, 7152, 8940, 11920, 17880, 35760.
What is 35760 in binary?
1000101110110000 (hexadecimal 8BB0, octal 105660).
What is the square root of 35760?
About 189.1031, exactly 4√2235.
Is 35760 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 35760?
It is a composite number with 40 divisors.