The number 77688
77688 is a composite number with 48 divisors. Its prime factorisation is × × 13 × 83. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72 … 77688.
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How to work it out
- 1
What is special about 77688: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.
- 2
77688 is composite. Its prime factorisation is
- 3
The divisors add up to 229320; without 77688 itself that is 151632, so 77688 is abundant (151632 is more than 77688). Euler's totient φ(77688) = 23616 numbers up to 77688 share no factor with it.
- 4
The digits of 77688 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77688 = 2^{3} \times 3^{2} \times 13 \times 83 \]77688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 229320 |
| Euler totient φ(n) | 23616 |
| Square | 6035425344 |
| Cube | 468880124124672 |
| Square root | 278.725672 (= 6√2158) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.7688 × |
77688 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred and eighty-eight |
| Binary (base 2) | 10010111101111000 |
| Octal (base 8) | 227570 |
| Hexadecimal (base 16) | 12F78 |
| Base 3 | 10221120100 |
| As time | 77688 seconds = 21 h 34 min 48 s |
Is 77688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77688 ÷ 2 = 38844) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77688 ÷ 3 = 25896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77688 ÷ 4 = 19422) | 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 (77688 ÷ 6 = 12948) | 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 (77688 ÷ 8 = 9711) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77688 ÷ 9 = 8632) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77688 ÷ 12 = 6474) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77688 a prime number?
No. 77688 = × × 13 × 83, so it is divisible by 2.
What are the factors of 77688?
1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 83, 104, 117, 156, 166, 234, 249, 312, 332, 468, 498, 664, 747, 936, 996, 1079, 1494, 1992, 2158, 2988, 3237, 4316, 5976, 6474, 8632, 9711, 12948, 19422, 25896, 38844, 77688.
What is 77688 in binary?
10010111101111000 (hexadecimal 12F78, octal 227570).
What is the square root of 77688?
About 278.7257, exactly 6√2158.
Is 77688 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 77688?
77688 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.