The number 77728
77728 is a composite number with 24 divisors. Its prime factorisation is × 7 × 347. Divisors (24): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 347, 694, 1388, 2429 … 77728.
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How to work it out
- 1
77728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77728 is composite. Its prime factorisation is
- 3
The divisors add up to 175392; without 77728 itself that is 97664, so 77728 is abundant (97664 is more than 77728). Euler's totient φ(77728) = 33216 numbers up to 77728 share no factor with it.
- 4
The digits of 77728 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77728 = 2^{5} \times 7 \times 347 \]77728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 175392 |
| Euler totient φ(n) | 33216 |
| Square | 6041641984 |
| Cube | 469604748132352 |
| Square root | 278.797417 (= 4√4858) |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7728 × |
77728 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and twenty-eight |
| Binary (base 2) | 10010111110100000 |
| Octal (base 8) | 227640 |
| Hexadecimal (base 16) | 12FA0 |
| Base 3 | 10221121211 |
| As time | 77728 seconds = 21 h 35 min 28 s |
Is 77728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77728 ÷ 2 = 38864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77728 ÷ 4 = 19432) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77728 ÷ 7 = 11104) | 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 (77728 ÷ 8 = 9716) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77728 a prime number?
No. 77728 = × 7 × 347, so it is divisible by 2.
What are the factors of 77728?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 347, 694, 1388, 2429, 2776, 4858, 5552, 9716, 11104, 19432, 38864, 77728.
What is 77728 in binary?
10010111110100000 (hexadecimal 12FA0, octal 227640).
What is the square root of 77728?
About 278.7974, exactly 4√4858.
Is 77728 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 77728?
It is a composite number with 24 divisors.