The number 83640
83640 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 17 × 41. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40 … 83640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
83640 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83640 is composite. Its prime factorisation is
- 3
The divisors add up to 272160; without 83640 itself that is 188520, so 83640 is abundant (188520 is more than 83640). Euler's totient φ(83640) = 20480 numbers up to 83640 share no factor with it.
- 4
The digits of 83640 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 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83640 = 2^{3} \times 3 \times 5 \times 17 \times 41 \]83640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 272160 |
| Euler totient φ(n) | 20480 |
| Square | 6995649600 |
| Cube | 585116132544000 |
| Square root | 289.205809 (= 2√20910) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.364 × |
83640 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand six hundred and forty |
| Binary (base 2) | 10100011010111000 |
| Octal (base 8) | 243270 |
| Hexadecimal (base 16) | 146B8 |
| Base 3 | 11020201210 |
| As time | 83640 seconds = 23 h 14 min 0 s |
Is 83640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83640 ÷ 2 = 41820) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83640 ÷ 3 = 27880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83640 ÷ 4 = 20910) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (83640 ÷ 5 = 16728) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83640 ÷ 6 = 13940) | 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 (83640 ÷ 8 = 10455) | 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 (83640 ÷ 10 = 8364) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83640 ÷ 12 = 6970) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83640 a prime number?
No. 83640 = × 3 × 5 × 17 × 41, so it is divisible by 2.
What are the factors of 83640?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 41, 51, 60, 68, 82, 85, 102, 120, 123, 136, 164, 170, 204, 205, 246, 255, 328, 340, 408, 410, 492, 510, 615, 680, 697, 820, 984, 1020, 1230, 1394, 1640, 2040, 2091, 2460, 2788, 3485, 4182, 4920, 5576, 6970, 8364, 10455, 13940, 16728, 20910, 27880, 41820, 83640.
What is 83640 in binary?
10100011010111000 (hexadecimal 146B8, octal 243270).
What is the square root of 83640?
About 289.2058, exactly 2√20910.
Is 83640 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 83640?
It is a composite number with 64 divisors.