The number 76788
76788 is a composite number with 36 divisors. Its prime factorisation is × × 79. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 79, 81, 108, 158, 162 … 76788.
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How to work it out
- 1
What is special about 76788: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.
- 2
76788 is composite. Its prime factorisation is
- 3
The divisors add up to 203840; without 76788 itself that is 127052, so 76788 is abundant (127052 is more than 76788). Euler's totient φ(76788) = 25272 numbers up to 76788 share no factor with it.
- 4
The digits of 76788 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 76788 = 2^{2} \times 3^{5} \times 79 \]76788 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 203840 |
| Euler totient φ(n) | 25272 |
| Square | 5896396944 |
| Cube | 452772528535872 |
| Square root | 277.106478 (= 18√237) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.6788 × |
76788 in other forms
| Form | Value |
|---|---|
| In words | seventy-six thousand seven hundred and eighty-eight |
| Binary (base 2) | 10010101111110100 |
| Octal (base 8) | 225764 |
| Hexadecimal (base 16) | 12BF4 |
| Base 3 | 10220100000 |
| As time | 76788 seconds = 21 h 19 min 48 s |
Is 76788 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (76788 ÷ 2 = 38394) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (76788 ÷ 3 = 25596) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (76788 ÷ 4 = 19197) | 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 (76788 ÷ 6 = 12798) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (76788 ÷ 9 = 8532) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (76788 ÷ 12 = 6399) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 76788 a prime number?
No. 76788 = × × 79, so it is divisible by 2.
What are the factors of 76788?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 79, 81, 108, 158, 162, 237, 243, 316, 324, 474, 486, 711, 948, 972, 1422, 2133, 2844, 4266, 6399, 8532, 12798, 19197, 25596, 38394, 76788.
What is 76788 in binary?
10010101111110100 (hexadecimal 12BF4, octal 225764).
What is the square root of 76788?
About 277.1065, exactly 18√237.
Is 76788 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 76788?
76788 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.