The number 42705
42705 is a composite number with 24 divisors. Its prime factorisation is × 5 × 13 × 73. Divisors (24): 1, 3, 5, 9, 13, 15, 39, 45, 65, 73, 117, 195, 219, 365, 585, 657 … 42705.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 42705: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
42705 is composite. Its prime factorisation is
- 3
The divisors add up to 80808; without 42705 itself that is 38103, so 42705 is deficient (38103 is less than 42705). Euler's totient φ(42705) = 20736 numbers up to 42705 share no factor with it.
- 4
The digits of 42705 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42705 = 3^{2} \times 5 \times 13 \times 73 \]42705 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 80808 |
| Euler totient φ(n) | 20736 |
| Square | 1823717025 |
| Cube | 77881835552625 |
| Square root | 206.651881 (= 3√4745) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 49 |
| Scientific notation | 4.2705 × |
42705 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand seven hundred and five |
| Binary (base 2) | 1010011011010001 |
| Octal (base 8) | 123321 |
| Hexadecimal (base 16) | A6D1 |
| Base 3 | 2011120200 |
| As time | 42705 seconds = 11 h 51 min 45 s |
Is 42705 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 (42705 ÷ 3 = 14235) | 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 | Yes (42705 ÷ 5 = 8541) | 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 5) | 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 | Yes (42705 ÷ 9 = 4745) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 42705 a prime number?
No. 42705 = × 5 × 13 × 73, so it is divisible by 3.
What are the factors of 42705?
1, 3, 5, 9, 13, 15, 39, 45, 65, 73, 117, 195, 219, 365, 585, 657, 949, 1095, 2847, 3285, 4745, 8541, 14235, 42705.
What is 42705 in binary?
1010011011010001 (hexadecimal A6D1, octal 123321).
What is the square root of 42705?
About 206.6519, exactly 3√4745.
Is 42705 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 42705?
42705 is a happy number: repeatedly adding the squares of its digits reaches 1.