The number 7776
7776 is a perfect power (). Its prime factorisation is × . Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 7776.
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How to work it out
- 1
What is special about 7776: a perfect power (); a Harshad number: divisible by its digit sum 27.
- 2
7776 is composite. Its prime factorisation is
- 3
The divisors add up to 22932; without 7776 itself that is 15156, so 7776 is abundant (15156 is more than 7776). Euler's totient φ(7776) = 2592 numbers up to 7776 share no factor with it.
- 4
The digits of 7776 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 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7776 = 2^{5} \times 3^{5} \]7776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 22932 |
| Euler totient φ(n) | 2592 |
| Square | 60466176 |
| Cube | 470184984576 |
| Square root | 88.181631 (= 36√6) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 101 |
| Scientific notation | 7.776 × |
| Perfect power |
7776 in other forms
| Form | Value |
|---|---|
| In words | seven thousand seven hundred and seventy-six |
| Binary (base 2) | 1111001100000 |
| Octal (base 8) | 17140 |
| Hexadecimal (base 16) | 1E60 |
| Base 3 | 101200000 |
| As time | 7776 seconds = 2 h 9 min 36 s |
Is 7776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7776 ÷ 2 = 3888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7776 ÷ 3 = 2592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7776 ÷ 4 = 1944) | 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 (7776 ÷ 6 = 1296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (7776 ÷ 8 = 972) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7776 ÷ 9 = 864) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7776 ÷ 12 = 648) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7776 a prime number?
No. 7776 = × , so it is divisible by 2.
What are the factors of 7776?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776.
What is 7776 in binary?
1111001100000 (hexadecimal 1E60, octal 17140).
What is the square root of 7776?
About 88.1816, exactly 36√6.
Is 7776 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 7776?
7776 is a perfect power (); a Harshad number: divisible by its digit sum 27.