The number 77832
77832 is a composite number with 48 divisors. Its prime factorisation is × × 23 × 47. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 47, 69, 72 … 77832.
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How to work it out
- 1
77832 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77832 is composite. Its prime factorisation is
- 3
The divisors add up to 224640; without 77832 itself that is 146808, so 77832 is abundant (146808 is more than 77832). Euler's totient φ(77832) = 24288 numbers up to 77832 share no factor with it.
- 4
The digits of 77832 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77832 = 2^{3} \times 3^{2} \times 23 \times 47 \]77832 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 224640 |
| Euler totient φ(n) | 24288 |
| Square | 6057820224 |
| Cube | 471492263674368 |
| Square root | 278.983871 (= 6√2162) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.7832 × |
77832 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and thirty-two |
| Binary (base 2) | 10011000000001000 |
| Octal (base 8) | 230010 |
| Hexadecimal (base 16) | 13008 |
| Base 3 | 10221202200 |
| As time | 77832 seconds = 21 h 37 min 12 s |
Is 77832 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77832 ÷ 2 = 38916) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77832 ÷ 3 = 25944) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77832 ÷ 4 = 19458) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77832 ÷ 6 = 12972) | 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 (77832 ÷ 8 = 9729) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77832 ÷ 9 = 8648) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77832 ÷ 12 = 6486) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77832 a prime number?
No. 77832 = × × 23 × 47, so it is divisible by 2.
What are the factors of 77832?
1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 47, 69, 72, 92, 94, 138, 141, 184, 188, 207, 276, 282, 376, 414, 423, 552, 564, 828, 846, 1081, 1128, 1656, 1692, 2162, 3243, 3384, 4324, 6486, 8648, 9729, 12972, 19458, 25944, 38916, 77832.
What is 77832 in binary?
10011000000001000 (hexadecimal 13008, octal 230010).
What is the square root of 77832?
About 278.9839, exactly 6√2162.
Is 77832 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77832?
It is a composite number with 48 divisors.