The number 42084
42084 is a composite number with 36 divisors. Its prime factorisation is × × 7 × 167. Divisors (36): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84 … 42084.
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How to work it out
- 1
What is special about 42084: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
42084 is composite. Its prime factorisation is
- 3
The divisors add up to 122304; without 42084 itself that is 80220, so 42084 is abundant (80220 is more than 42084). Euler's totient φ(42084) = 11952 numbers up to 42084 share no factor with it.
- 4
The digits of 42084 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 106 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42084 = 2^{2} \times 3^{2} \times 7 \times 167 \]42084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 122304 |
| Euler totient φ(n) | 11952 |
| Square | 1771063056 |
| Cube | 74533417648704 |
| Square root | 205.143852 (= 6√1169) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 106 |
| Scientific notation | 4.2084 × |
42084 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand and eighty-four |
| Binary (base 2) | 1010010001100100 |
| Octal (base 8) | 122144 |
| Hexadecimal (base 16) | A464 |
| Base 3 | 2010201200 |
| As time | 42084 seconds = 11 h 41 min 24 s |
Is 42084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42084 ÷ 2 = 21042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42084 ÷ 3 = 14028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42084 ÷ 4 = 10521) | 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 | Yes (42084 ÷ 6 = 7014) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (42084 ÷ 7 = 6012) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (42084 ÷ 9 = 4676) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42084 ÷ 12 = 3507) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42084 a prime number?
No. 42084 = × × 7 × 167, so it is divisible by 2.
What are the factors of 42084?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 167, 252, 334, 501, 668, 1002, 1169, 1503, 2004, 2338, 3006, 3507, 4676, 6012, 7014, 10521, 14028, 21042, 42084.
What is 42084 in binary?
1010010001100100 (hexadecimal A464, octal 122144).
What is the square root of 42084?
About 205.1439, exactly 6√1169.
Is 42084 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 42084?
42084 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.