The number 83997
83997 is a composite number with 20 divisors. Its prime factorisation is × 17 × 61. Divisors (20): 1, 3, 9, 17, 27, 51, 61, 81, 153, 183, 459, 549, 1037, 1377, 1647, 3111 … 83997.
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How to work it out
- 1
83997 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83997 is composite. Its prime factorisation is
- 3
The divisors add up to 135036; without 83997 itself that is 51039, so 83997 is deficient (51039 is less than 83997). Euler's totient φ(83997) = 51840 numbers up to 83997 share no factor with it.
- 4
The digits of 83997 add up to 36, 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
\[ 83997 = 3^{4} \times 17 \times 61 \]83997 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 135036 |
| Euler totient φ(n) | 51840 |
| Square | 7055496009 |
| Cube | 592640498267973 |
| Square root | 289.822359 (= 9√1037) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3997 × |
83997 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and ninety-seven |
| Binary (base 2) | 10100100000011101 |
| Octal (base 8) | 244035 |
| Hexadecimal (base 16) | 1481D |
| Base 3 | 11021020000 |
| As time | 83997 seconds = 23 h 19 min 57 s |
Is 83997 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 | Yes (83997 ÷ 3 = 27999) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83997 ÷ 9 = 9333) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83997 a prime number?
No. 83997 = × 17 × 61, so it is divisible by 3.
What are the factors of 83997?
1, 3, 9, 17, 27, 51, 61, 81, 153, 183, 459, 549, 1037, 1377, 1647, 3111, 4941, 9333, 27999, 83997.
What is 83997 in binary?
10100100000011101 (hexadecimal 1481D, octal 244035).
What is the square root of 83997?
About 289.8224, exactly 9√1037.
Is 83997 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 83997?
It is a composite number with 20 divisors.