The number 83709
83709 is a composite number with 12 divisors. Its prime factorisation is × 71 × 131. Divisors (12): 1, 3, 9, 71, 131, 213, 393, 639, 1179, 9301, 27903, 83709.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83709: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83709 is composite. Its prime factorisation is
- 3
The divisors add up to 123552; without 83709 itself that is 39843, so 83709 is deficient (39843 is less than 83709). Euler's totient φ(83709) = 54600 numbers up to 83709 share no factor with it.
- 4
The digits of 83709 add up to 27, 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
\[ 83709 = 3^{2} \times 71 \times 131 \]83709 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 123552 |
| Euler totient φ(n) | 54600 |
| Square | 7007196681 |
| Cube | 586565426969829 |
| Square root | 289.325077 (= 3√9301) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3709 × |
83709 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand seven hundred and nine |
| Binary (base 2) | 10100011011111101 |
| Octal (base 8) | 243375 |
| Hexadecimal (base 16) | 146FD |
| Base 3 | 11020211100 |
| As time | 83709 seconds = 23 h 15 min 9 s |
Is 83709 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 (83709 ÷ 3 = 27903) | 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 4) | 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 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83709 ÷ 9 = 9301) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 83709 a prime number?
No. 83709 = × 71 × 131, so it is divisible by 3.
What are the factors of 83709?
1, 3, 9, 71, 131, 213, 393, 639, 1179, 9301, 27903, 83709.
What is 83709 in binary?
10100011011111101 (hexadecimal 146FD, octal 243375).
What is the square root of 83709?
About 289.3251, exactly 3√9301.
Is 83709 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 83709?
83709 is a happy number: repeatedly adding the squares of its digits reaches 1.