The number 87024
87024 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 37. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 37, 42, 48 … 87024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 87024: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
87024 is composite. Its prime factorisation is
- 3
The divisors add up to 268584; without 87024 itself that is 181560, so 87024 is abundant (181560 is more than 87024). Euler's totient φ(87024) = 24192 numbers up to 87024 share no factor with it.
- 4
The digits of 87024 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87024 = 2^{4} \times 3 \times 7^{2} \times 37 \]87024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 268584 |
| Euler totient φ(n) | 24192 |
| Square | 7573176576 |
| Cube | 659048118349824 |
| Square root | 294.998305 (= 28√111) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.7024 × |
87024 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand and twenty-four |
| Binary (base 2) | 10101001111110000 |
| Octal (base 8) | 251760 |
| Hexadecimal (base 16) | 153F0 |
| Base 3 | 11102101010 |
| As time | 87024 seconds = 24 h 10 min 24 s |
Is 87024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87024 ÷ 2 = 43512) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87024 ÷ 3 = 29008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87024 ÷ 4 = 21756) | 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 (87024 ÷ 6 = 14504) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (87024 ÷ 7 = 12432) | 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 | Yes (87024 ÷ 8 = 10878) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87024 ÷ 12 = 7252) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87024 a prime number?
No. 87024 = × 3 × × 37, so it is divisible by 2.
What are the factors of 87024?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 37, 42, 48, 49, 56, 74, 84, 98, 111, 112, 147, 148, 168, 196, 222, 259, 294, 296, 336, 392, 444, 518, 588, 592, 777, 784, 888, 1036, 1176, 1554, 1776, 1813, 2072, 2352, 3108, 3626, 4144, 5439, 6216, 7252, 10878, 12432, 14504, 21756, 29008, 43512, 87024.
What is 87024 in binary?
10101001111110000 (hexadecimal 153F0, octal 251760).
What is the square root of 87024?
About 294.9983, exactly 28√111.
Is 87024 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 87024?
87024 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.