The number 87084
87084 is a composite number with 36 divisors. Its prime factorisation is × × 41 × 59. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 36, 41, 59, 82, 118, 123, 164, 177 … 87084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 87084: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
87084 is composite. Its prime factorisation is
- 3
The divisors add up to 229320; without 87084 itself that is 142236, so 87084 is abundant (142236 is more than 87084). Euler's totient φ(87084) = 27840 numbers up to 87084 share no factor with it.
- 4
The digits of 87084 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 195 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87084 = 2^{2} \times 3^{2} \times 41 \times 59 \]87084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 229320 |
| Euler totient φ(n) | 27840 |
| Square | 7583623056 |
| Cube | 660412230208704 |
| Square root | 295.099983 (= 6√2419) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 195 |
| Scientific notation | 8.7084 × |
87084 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand and eighty-four |
| Binary (base 2) | 10101010000101100 |
| Octal (base 8) | 252054 |
| Hexadecimal (base 16) | 1542C |
| Base 3 | 11102110100 |
| As time | 87084 seconds = 24 h 11 min 24 s |
Is 87084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87084 ÷ 2 = 43542) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87084 ÷ 3 = 29028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87084 ÷ 4 = 21771) | 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 (87084 ÷ 6 = 14514) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (87084 ÷ 9 = 9676) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87084 ÷ 12 = 7257) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87084 a prime number?
No. 87084 = × × 41 × 59, so it is divisible by 2.
What are the factors of 87084?
1, 2, 3, 4, 6, 9, 12, 18, 36, 41, 59, 82, 118, 123, 164, 177, 236, 246, 354, 369, 492, 531, 708, 738, 1062, 1476, 2124, 2419, 4838, 7257, 9676, 14514, 21771, 29028, 43542, 87084.
What is 87084 in binary?
10101010000101100 (hexadecimal 1542C, octal 252054).
What is the square root of 87084?
About 295.1000, exactly 6√2419.
Is 87084 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 87084?
87084 is a happy number: repeatedly adding the squares of its digits reaches 1.