The number 7788
7788 is a composite number with 24 divisors. Its prime factorisation is × 3 × 11 × 59. Divisors (24): 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 59, 66, 118, 132, 177, 236 … 7788.
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How to work it out
- 1
What is special about 7788: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7788 is composite. Its prime factorisation is
- 3
The divisors add up to 20160; without 7788 itself that is 12372, so 7788 is abundant (12372 is more than 7788). Euler's totient φ(7788) = 2320 numbers up to 7788 share no factor with it.
- 4
The digits of 7788 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 83 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7788 = 2^{2} \times 3 \times 11 \times 59 \]7788 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 20160 |
| Euler totient φ(n) | 2320 |
| Square | 60652944 |
| Cube | 472365127872 |
| Square root | 88.249646 (= 2√1947) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 83 |
| Scientific notation | 7.788 × |
7788 in other forms
| Form | Value |
|---|---|
| In words | seven thousand seven hundred and eighty-eight |
| Binary (base 2) | 1111001101100 |
| Octal (base 8) | 17154 |
| Hexadecimal (base 16) | 1E6C |
| Base 3 | 101200110 |
| As time | 7788 seconds = 2 h 9 min 48 s |
Is 7788 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7788 ÷ 2 = 3894) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7788 ÷ 3 = 2596) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7788 ÷ 4 = 1947) | 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 (7788 ÷ 6 = 1298) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (7788 ÷ 11 = 708) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7788 ÷ 12 = 649) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7788 a prime number?
No. 7788 = × 3 × 11 × 59, so it is divisible by 2.
What are the factors of 7788?
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 59, 66, 118, 132, 177, 236, 354, 649, 708, 1298, 1947, 2596, 3894, 7788.
What is 7788 in binary?
1111001101100 (hexadecimal 1E6C, octal 17154).
What is the square root of 7788?
About 88.2496, exactly 2√1947.
Is 7788 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 7788?
7788 is a happy number: repeatedly adding the squares of its digits reaches 1.