The number 83760
83760 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 349. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 83760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83760: a Harshad number: divisible by its digit sum 24.
- 2
83760 is composite. Its prime factorisation is
- 3
The divisors add up to 260400; without 83760 itself that is 176640, so 83760 is abundant (176640 is more than 83760). Euler's totient φ(83760) = 22272 numbers up to 83760 share no factor with it.
- 4
The digits of 83760 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83760 = 2^{4} \times 3 \times 5 \times 349 \]83760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 260400 |
| Euler totient φ(n) | 22272 |
| Square | 7015737600 |
| Cube | 587638181376000 |
| Square root | 289.413199 (= 4√5235) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.376 × |
83760 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand seven hundred and sixty |
| Binary (base 2) | 10100011100110000 |
| Octal (base 8) | 243460 |
| Hexadecimal (base 16) | 14730 |
| Base 3 | 11020220020 |
| As time | 83760 seconds = 23 h 16 min 0 s |
Is 83760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83760 ÷ 2 = 41880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83760 ÷ 3 = 27920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83760 ÷ 4 = 20940) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (83760 ÷ 5 = 16752) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83760 ÷ 6 = 13960) | 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 (83760 ÷ 8 = 10470) | 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 (83760 ÷ 10 = 8376) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83760 ÷ 12 = 6980) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83760 a prime number?
No. 83760 = × 3 × 5 × 349, so it is divisible by 2.
What are the factors of 83760?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 349, 698, 1047, 1396, 1745, 2094, 2792, 3490, 4188, 5235, 5584, 6980, 8376, 10470, 13960, 16752, 20940, 27920, 41880, 83760.
What is 83760 in binary?
10100011100110000 (hexadecimal 14730, octal 243460).
What is the square root of 83760?
About 289.4132, exactly 4√5235.
Is 83760 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 83760?
83760 is a Harshad number: divisible by its digit sum 24.