The number 42405
42405 is a binary palindrome (1010010110100101). Its prime factorisation is 3 × 5 × 11 × 257. Divisors (16): 1, 3, 5, 11, 15, 33, 55, 165, 257, 771, 1285, 2827, 3855, 8481, 14135, 42405.
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How to work it out
- 1
What is special about 42405: a binary palindrome (1010010110100101); a Harshad number: divisible by its digit sum 15.
- 2
42405 is composite. Its prime factorisation is
- 3
The divisors add up to 74304; without 42405 itself that is 31899, so 42405 is deficient (31899 is less than 42405). Euler's totient φ(42405) = 20480 numbers up to 42405 share no factor with it.
- 4
The digits of 42405 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 57 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42405 = 3 \times 5 \times 11 \times 257 \]
42405 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 74304 |
| Euler totient φ(n) | 20480 |
| Square | 1798184025 |
| Cube | 76251993580125 |
| Square root | 205.924744 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 57 |
| Scientific notation | 4.2405 × |
42405 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand four hundred and five |
| Binary (base 2) | 1010010110100101 |
| Octal (base 8) | 122645 |
| Hexadecimal (base 16) | A5A5 |
| Base 3 | 2011011120 |
| As time | 42405 seconds = 11 h 46 min 45 s |
Is 42405 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 (42405 ÷ 3 = 14135) | 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 (42405 ÷ 5 = 8481) | 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 6) | 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 | No (remainder 6) | 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 | Yes (42405 ÷ 11 = 3855) | 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 42405 a prime number?
No. 42405 = 3 × 5 × 11 × 257, so it is divisible by 3.
What are the factors of 42405?
1, 3, 5, 11, 15, 33, 55, 165, 257, 771, 1285, 2827, 3855, 8481, 14135, 42405.
What is 42405 in binary?
1010010110100101 (hexadecimal A5A5, octal 122645).
What is the square root of 42405?
About 205.9247.
Is 42405 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 42405?
42405 is a binary palindrome (1010010110100101); a Harshad number: divisible by its digit sum 15.