The number 77868
77868 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 103. Divisors (48): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54 … 77868.
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How to work it out
- 1
What is special about 77868: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.
- 2
77868 is composite. Its prime factorisation is
- 3
The divisors add up to 232960; without 77868 itself that is 155092, so 77868 is abundant (155092 is more than 77868). Euler's totient φ(77868) = 22032 numbers up to 77868 share no factor with it.
- 4
The digits of 77868 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 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77868 = 2^{2} \times 3^{3} \times 7 \times 103 \]77868 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 232960 |
| Euler totient φ(n) | 22032 |
| Square | 6063425424 |
| Cube | 472146810916032 |
| Square root | 279.048383 (= 6√2163) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7868 × |
77868 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and sixty-eight |
| Binary (base 2) | 10011000000101100 |
| Octal (base 8) | 230054 |
| Hexadecimal (base 16) | 1302C |
| Base 3 | 10221211000 |
| As time | 77868 seconds = 21 h 37 min 48 s |
Is 77868 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77868 ÷ 2 = 38934) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77868 ÷ 3 = 25956) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77868 ÷ 4 = 19467) | 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 (77868 ÷ 6 = 12978) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77868 ÷ 7 = 11124) | 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 (77868 ÷ 9 = 8652) | 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 (77868 ÷ 12 = 6489) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77868 a prime number?
No. 77868 = × × 7 × 103, so it is divisible by 2.
What are the factors of 77868?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 103, 108, 126, 189, 206, 252, 309, 378, 412, 618, 721, 756, 927, 1236, 1442, 1854, 2163, 2781, 2884, 3708, 4326, 5562, 6489, 8652, 11124, 12978, 19467, 25956, 38934, 77868.
What is 77868 in binary?
10011000000101100 (hexadecimal 1302C, octal 230054).
What is the square root of 77868?
About 279.0484, exactly 6√2163.
Is 77868 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 77868?
77868 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 36.