The number 83160
83160 is a highly composite number: it has 128 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7 × 11. Divisors (128): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20 … 83160.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83160: a highly composite number: it has 128 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.
- 2
83160 is composite. Its prime factorisation is
- 3
The divisors add up to 345600; without 83160 itself that is 262440, so 83160 is abundant (262440 is more than 83160). Euler's totient φ(83160) = 17280 numbers up to 83160 share no factor with it.
- 4
The digits of 83160 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83160 = 2^{3} \times 3^{3} \times 5 \times 7 \times 11 \]83160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 128 |
| Sum of divisors | 345600 |
| Euler totient φ(n) | 17280 |
| Square | 6915585600 |
| Cube | 575100098496000 |
| Square root | 288.374756 (= 6√2310) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.316 × |
83160 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand one hundred and sixty |
| Binary (base 2) | 10100010011011000 |
| Octal (base 8) | 242330 |
| Hexadecimal (base 16) | 144D8 |
| Base 3 | 11020002000 |
| As time | 83160 seconds = 23 h 6 min 0 s |
Is 83160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83160 ÷ 2 = 41580) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83160 ÷ 3 = 27720) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83160 ÷ 4 = 20790) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (83160 ÷ 5 = 16632) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83160 ÷ 6 = 13860) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (83160 ÷ 7 = 11880) | 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 (83160 ÷ 8 = 10395) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83160 ÷ 9 = 9240) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (83160 ÷ 10 = 8316) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (83160 ÷ 11 = 7560) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83160 ÷ 12 = 6930) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83160 a prime number?
No. 83160 = × × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 83160?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 40, 42, 44, 45, 54, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 108, 110, 120, 126, 132, 135, 140, 154, 165, 168, 180, 189, 198, 210, 216, 220, 231, 252, 264, 270, 280, 297, 308, 315, 330, 360, 378, 385, 396, 420, 440, 462, 495, 504, 540, 594, 616, 630, 660, 693, 756, 770, 792, 840, 924, 945, 990, 1080, 1155, 1188, 1260, 1320, 1386, 1485, 1512, 1540, 1848, 1890, 1980, 2079, 2310, 2376, 2520, 2772, 2970, 3080, 3465, 3780, 3960, 4158, 4620, 5544, 5940, 6930, 7560, 8316, 9240, 10395, 11880, 13860, 16632, 20790, 27720, 41580, 83160.
What is 83160 in binary?
10100010011011000 (hexadecimal 144D8, octal 242330).
What is the square root of 83160?
About 288.3748, exactly 6√2310.
Is 83160 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 83160?
83160 is a highly composite number: it has 128 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.