The number 87768
87768 is a composite number with 48 divisors. Its prime factorisation is × × 23 × 53. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 53, 69, 72 … 87768.
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How to work it out
- 1
What is special about 87768: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.
- 2
87768 is composite. Its prime factorisation is
- 3
The divisors add up to 252720; without 87768 itself that is 164952, so 87768 is abundant (164952 is more than 87768). Euler's totient φ(87768) = 27456 numbers up to 87768 share no factor with it.
- 4
The digits of 87768 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 270 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87768 = 2^{3} \times 3^{2} \times 23 \times 53 \]87768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 252720 |
| Euler totient φ(n) | 27456 |
| Square | 7703221824 |
| Cube | 676096373048832 |
| Square root | 296.256645 (= 6√2438) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 270 |
| Scientific notation | 8.7768 × |
87768 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand seven hundred and sixty-eight |
| Binary (base 2) | 10101011011011000 |
| Octal (base 8) | 253330 |
| Hexadecimal (base 16) | 156D8 |
| Base 3 | 11110101200 |
| As time | 87768 seconds = 24 h 22 min 48 s |
Is 87768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87768 ÷ 2 = 43884) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87768 ÷ 3 = 29256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87768 ÷ 4 = 21942) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87768 ÷ 6 = 14628) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (87768 ÷ 8 = 10971) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (87768 ÷ 9 = 9752) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87768 ÷ 12 = 7314) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87768 a prime number?
No. 87768 = × × 23 × 53, so it is divisible by 2.
What are the factors of 87768?
1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 53, 69, 72, 92, 106, 138, 159, 184, 207, 212, 276, 318, 414, 424, 477, 552, 636, 828, 954, 1219, 1272, 1656, 1908, 2438, 3657, 3816, 4876, 7314, 9752, 10971, 14628, 21942, 29256, 43884, 87768.
What is 87768 in binary?
10101011011011000 (hexadecimal 156D8, octal 253330).
What is the square root of 87768?
About 296.2566, exactly 6√2438.
Is 87768 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 87768?
87768 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.