The number 87564
87564 is a composite number with 12 divisors. Its prime factorisation is × 3 × 7297. Divisors (12): 1, 2, 3, 4, 6, 12, 7297, 14594, 21891, 29188, 43782, 87564.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 87564: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
87564 is composite. Its prime factorisation is
- 3
The divisors add up to 204344; without 87564 itself that is 116780, so 87564 is abundant (116780 is more than 87564). Euler's totient φ(87564) = 29184 numbers up to 87564 share no factor with it.
- 4
The digits of 87564 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87564 = 2^{2} \times 3 \times 7297 \]87564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 204344 |
| Euler totient φ(n) | 29184 |
| Square | 7667454096 |
| Cube | 671392950462144 |
| Square root | 295.912149 (= 2√21891) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.7564 × |
87564 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand five hundred and sixty-four |
| Binary (base 2) | 10101011000001100 |
| Octal (base 8) | 253014 |
| Hexadecimal (base 16) | 1560C |
| Base 3 | 11110010010 |
| As time | 87564 seconds = 24 h 19 min 24 s |
Is 87564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87564 ÷ 2 = 43782) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87564 ÷ 3 = 29188) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87564 ÷ 4 = 21891) | 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 (87564 ÷ 6 = 14594) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | No (remainder 3) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87564 ÷ 12 = 7297) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87564 a prime number?
No. 87564 = × 3 × 7297, so it is divisible by 2.
What are the factors of 87564?
1, 2, 3, 4, 6, 12, 7297, 14594, 21891, 29188, 43782, 87564.
What is 87564 in binary?
10101011000001100 (hexadecimal 1560C, octal 253014).
What is the square root of 87564?
About 295.9121, exactly 2√21891.
Is 87564 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 87564?
87564 is a happy number: repeatedly adding the squares of its digits reaches 1.