The number 7728
7728 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 23. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46 … 7728.
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How to work it out
- 1
What is special about 7728: a Harshad number: divisible by its digit sum 24.
- 2
7728 is composite. Its prime factorisation is
- 3
The divisors add up to 23808; without 7728 itself that is 16080, so 7728 is abundant (16080 is more than 7728). Euler's totient φ(7728) = 2112 numbers up to 7728 share no factor with it.
- 4
The digits of 7728 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7728 = 2^{4} \times 3 \times 7 \times 23 \]7728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 23808 |
| Euler totient φ(n) | 2112 |
| Square | 59721984 |
| Cube | 461531492352 |
| Square root | 87.909044 (= 4√483) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 26 |
| Scientific notation | 7.728 × |
7728 in other forms
| Form | Value |
|---|---|
| In words | seven thousand seven hundred and twenty-eight |
| Binary (base 2) | 1111000110000 |
| Octal (base 8) | 17060 |
| Hexadecimal (base 16) | 1E30 |
| Base 3 | 101121020 |
| As time | 7728 seconds = 2 h 8 min 48 s |
Is 7728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7728 ÷ 2 = 3864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7728 ÷ 3 = 2576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7728 ÷ 4 = 1932) | 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 (7728 ÷ 6 = 1288) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7728 ÷ 7 = 1104) | 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 (7728 ÷ 8 = 966) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 (7728 ÷ 12 = 644) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7728 a prime number?
No. 7728 = × 3 × 7 × 23, so it is divisible by 2.
What are the factors of 7728?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728.
What is 7728 in binary?
1111000110000 (hexadecimal 1E30, octal 17060).
What is the square root of 7728?
About 87.9090, exactly 4√483.
Is 7728 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 7728?
7728 is a Harshad number: divisible by its digit sum 24.