The number 83521
83521 is a perfect power () and a perfect square (289²). Its prime factorisation is . Divisors (5): 1, 17, 289, 4913, 83521.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83521: a perfect power (); a perfect square (289²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83521 is composite. Its prime factorisation is
- 3
The divisors add up to 88741; without 83521 itself that is 5220, so 83521 is deficient (5220 is less than 83521). Euler's totient φ(83521) = 78608 numbers up to 83521 share no factor with it.
- 4
The digits of 83521 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83521 = 17^{4} \]83521 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 5 |
| Sum of divisors | 88741 |
| Euler totient φ(n) | 78608 |
| Square | 6975757441 |
| Cube | 582622237229761 |
| Square root | 289 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3521 × |
| Perfect power |
83521 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand five hundred and twenty-one |
| Binary (base 2) | 10100011001000001 |
| Octal (base 8) | 243101 |
| Hexadecimal (base 16) | 14641 |
| Base 3 | 11020120101 |
| As time | 83521 seconds = 23 h 12 min 1 s |
Is 83521 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83521 a prime number?
No. 83521 = , so it is divisible by 17.
What are the factors of 83521?
1, 17, 289, 4913, 83521.
What is 83521 in binary?
10100011001000001 (hexadecimal 14641, octal 243101).
What is the square root of 83521?
289, because 289 × 289 = 83521.
Is 83521 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 83521?
83521 is a perfect power (); a perfect square (289²); a happy number: repeatedly adding the squares of its digits reaches 1.