The number 87216
87216 is a composite number with 40 divisors. Its prime factorisation is × 3 × 23 × 79. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 69, 79, 92, 138 … 87216.
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How to work it out
- 1
What is special about 87216: a Harshad number: divisible by its digit sum 24.
- 2
87216 is composite. Its prime factorisation is
- 3
The divisors add up to 238080; without 87216 itself that is 150864, so 87216 is abundant (150864 is more than 87216). Euler's totient φ(87216) = 27456 numbers up to 87216 share no factor with it.
- 4
The digits of 87216 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87216 = 2^{4} \times 3 \times 23 \times 79 \]87216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 238080 |
| Euler totient φ(n) | 27456 |
| Square | 7606630656 |
| Cube | 663419899293696 |
| Square root | 295.323551 (= 4√5451) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.7216 × |
87216 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand two hundred and sixteen |
| Binary (base 2) | 10101010010110000 |
| Octal (base 8) | 252260 |
| Hexadecimal (base 16) | 154B0 |
| Base 3 | 11102122020 |
| As time | 87216 seconds = 24 h 13 min 36 s |
Is 87216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87216 ÷ 2 = 43608) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87216 ÷ 3 = 29072) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87216 ÷ 4 = 21804) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87216 ÷ 6 = 14536) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (87216 ÷ 8 = 10902) | 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 6) | 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 (87216 ÷ 12 = 7268) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87216 a prime number?
No. 87216 = × 3 × 23 × 79, so it is divisible by 2.
What are the factors of 87216?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 69, 79, 92, 138, 158, 184, 237, 276, 316, 368, 474, 552, 632, 948, 1104, 1264, 1817, 1896, 3634, 3792, 5451, 7268, 10902, 14536, 21804, 29072, 43608, 87216.
What is 87216 in binary?
10101010010110000 (hexadecimal 154B0, octal 252260).
What is the square root of 87216?
About 295.3236, exactly 4√5451.
Is 87216 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 87216?
87216 is a Harshad number: divisible by its digit sum 24.