The number 77328
77328 is a composite number with 40 divisors. Its prime factorisation is × × 179. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 77328.
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How to work it out
- 1
What is special about 77328: a Harshad number: divisible by its digit sum 27.
- 2
77328 is composite. Its prime factorisation is
- 3
The divisors add up to 223200; without 77328 itself that is 145872, so 77328 is abundant (145872 is more than 77328). Euler's totient φ(77328) = 25632 numbers up to 77328 share no factor with it.
- 4
The digits of 77328 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 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77328 = 2^{4} \times 3^{3} \times 179 \]77328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 223200 |
| Euler totient φ(n) | 25632 |
| Square | 5979619584 |
| Cube | 462392023191552 |
| Square root | 278.079125 (= 12√537) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.7328 × |
77328 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand three hundred and twenty-eight |
| Binary (base 2) | 10010111000010000 |
| Octal (base 8) | 227020 |
| Hexadecimal (base 16) | 12E10 |
| Base 3 | 10221002000 |
| As time | 77328 seconds = 21 h 28 min 48 s |
Is 77328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77328 ÷ 2 = 38664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77328 ÷ 3 = 25776) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77328 ÷ 4 = 19332) | 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 (77328 ÷ 6 = 12888) | 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 (77328 ÷ 8 = 9666) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77328 ÷ 9 = 8592) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77328 ÷ 12 = 6444) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77328 a prime number?
No. 77328 = × × 179, so it is divisible by 2.
What are the factors of 77328?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 179, 216, 358, 432, 537, 716, 1074, 1432, 1611, 2148, 2864, 3222, 4296, 4833, 6444, 8592, 9666, 12888, 19332, 25776, 38664, 77328.
What is 77328 in binary?
10010111000010000 (hexadecimal 12E10, octal 227020).
What is the square root of 77328?
About 278.0791, exactly 12√537.
Is 77328 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77328?
77328 is a Harshad number: divisible by its digit sum 27.