The number 73689
73689 is a composite number with 24 divisors. Its prime factorisation is 3 × 7 × × 29. Divisors (24): 1, 3, 7, 11, 21, 29, 33, 77, 87, 121, 203, 231, 319, 363, 609, 847 … 73689.
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How to work it out
- 1
What is special about 73689: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 33.
- 2
73689 is composite. Its prime factorisation is
- 3
The divisors add up to 127680; without 73689 itself that is 53991, so 73689 is deficient (53991 is less than 73689). Euler's totient φ(73689) = 36960 numbers up to 73689 share no factor with it.
- 4
The digits of 73689 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73689 = 3 \times 7 \times 11^{2} \times 29 \]73689 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 127680 |
| Euler totient φ(n) | 36960 |
| Square | 5430068721 |
| Cube | 400136333981769 |
| Square root | 271.457179 (= 11√609) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.3689 × |
73689 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand six hundred and eighty-nine |
| Binary (base 2) | 10001111111011001 |
| Octal (base 8) | 217731 |
| Hexadecimal (base 16) | 11FD9 |
| Base 3 | 10202002020 |
| As time | 73689 seconds = 20 h 28 min 9 s |
Is 73689 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 (73689 ÷ 3 = 24563) | 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 | Yes (73689 ÷ 7 = 10527) | 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 6) | 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 | Yes (73689 ÷ 11 = 6699) | 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 73689 a prime number?
No. 73689 = 3 × 7 × × 29, so it is divisible by 3.
What are the factors of 73689?
1, 3, 7, 11, 21, 29, 33, 77, 87, 121, 203, 231, 319, 363, 609, 847, 957, 2233, 2541, 3509, 6699, 10527, 24563, 73689.
What is 73689 in binary?
10001111111011001 (hexadecimal 11FD9, octal 217731).
What is the square root of 73689?
About 271.4572, exactly 11√609.
Is 73689 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 73689?
73689 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 33.