The number 83006
83006 is a composite number with 24 divisors. Its prime factorisation is 2 × × . Divisors (24): 1, 2, 7, 11, 14, 22, 49, 77, 98, 121, 154, 242, 343, 539, 686, 847 … 83006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83006: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83006 is composite. Its prime factorisation is
- 3
The divisors add up to 159600; without 83006 itself that is 76594, so 83006 is deficient (76594 is less than 83006). Euler's totient φ(83006) = 32340 numbers up to 83006 share no factor with it.
- 4
The digits of 83006 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83006 = 2 \times 7^{3} \times 11^{2} \]83006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 159600 |
| Euler totient φ(n) | 32340 |
| Square | 6889996036 |
| Cube | 571911010964216 |
| Square root | 288.107619 (= 77√14) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3006 × |
83006 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand and six |
| Binary (base 2) | 10100010000111110 |
| Octal (base 8) | 242076 |
| Hexadecimal (base 16) | 1443E |
| Base 3 | 11012212022 |
| As time | 83006 seconds = 23 h 3 min 26 s |
Is 83006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83006 ÷ 2 = 41503) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (83006 ÷ 7 = 11858) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (83006 ÷ 11 = 7546) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83006 a prime number?
No. 83006 = 2 × × , so it is divisible by 2.
What are the factors of 83006?
1, 2, 7, 11, 14, 22, 49, 77, 98, 121, 154, 242, 343, 539, 686, 847, 1078, 1694, 3773, 5929, 7546, 11858, 41503, 83006.
What is 83006 in binary?
10100010000111110 (hexadecimal 1443E, octal 242076).
What is the square root of 83006?
About 288.1076, exactly 77√14.
Is 83006 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 83006?
83006 is a happy number: repeatedly adding the squares of its digits reaches 1.