The number 83520
83520 is a composite number with 84 divisors. Its prime factorisation is × × 5 × 29. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29 … 83520.
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How to work it out
- 1
What is special about 83520: a Harshad number: divisible by its digit sum 18.
- 2
83520 is composite. Its prime factorisation is
- 3
The divisors add up to 297180; without 83520 itself that is 213660, so 83520 is abundant (213660 is more than 83520). Euler's totient φ(83520) = 21504 numbers up to 83520 share no factor with it.
- 4
The digits of 83520 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 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83520 = 2^{6} \times 3^{2} \times 5 \times 29 \]83520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 297180 |
| Euler totient φ(n) | 21504 |
| Square | 6975590400 |
| Cube | 582601310208000 |
| Square root | 288.998270 (= 24√145) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.352 × |
83520 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand five hundred and twenty |
| Binary (base 2) | 10100011001000000 |
| Octal (base 8) | 243100 |
| Hexadecimal (base 16) | 14640 |
| Base 3 | 11020120100 |
| As time | 83520 seconds = 23 h 12 min 0 s |
Is 83520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83520 ÷ 2 = 41760) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83520 ÷ 3 = 27840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83520 ÷ 4 = 20880) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (83520 ÷ 5 = 16704) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83520 ÷ 6 = 13920) | 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 (83520 ÷ 8 = 10440) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83520 ÷ 9 = 9280) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (83520 ÷ 10 = 8352) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83520 ÷ 12 = 6960) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83520 a prime number?
No. 83520 = × × 5 × 29, so it is divisible by 2.
What are the factors of 83520?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 30, 32, 36, 40, 45, 48, 58, 60, 64, 72, 80, 87, 90, 96, 116, 120, 144, 145, 160, 174, 180, 192, 232, 240, 261, 288, 290, 320, 348, 360, 435, 464, 480, 522, 576, 580, 696, 720, 870, 928, 960, 1044, 1160, 1305, 1392, 1440, 1740, 1856, 2088, 2320, 2610, 2784, 2880, 3480, 4176, 4640, 5220, 5568, 6960, 8352, 9280, 10440, 13920, 16704, 20880, 27840, 41760, 83520.
What is 83520 in binary?
10100011001000000 (hexadecimal 14640, octal 243100).
What is the square root of 83520?
About 288.9983, exactly 24√145.
Is 83520 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 83520?
83520 is a Harshad number: divisible by its digit sum 18.