The number 77648
77648 is a composite number with 20 divisors. Its prime factorisation is × 23 × 211. Divisors (20): 1, 2, 4, 8, 16, 23, 46, 92, 184, 211, 368, 422, 844, 1688, 3376, 4853 … 77648.
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How to work it out
- 1
77648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77648 is composite. Its prime factorisation is
- 3
The divisors add up to 157728; without 77648 itself that is 80080, so 77648 is abundant (80080 is more than 77648). Euler's totient φ(77648) = 36960 numbers up to 77648 share no factor with it.
- 4
The digits of 77648 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77648 = 2^{4} \times 23 \times 211 \]77648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 157728 |
| Euler totient φ(n) | 36960 |
| Square | 6029211904 |
| Cube | 468156245921792 |
| Square root | 278.653907 (= 4√4853) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7648 × |
77648 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred and forty-eight |
| Binary (base 2) | 10010111101010000 |
| Octal (base 8) | 227520 |
| Hexadecimal (base 16) | 12F50 |
| Base 3 | 10221111212 |
| As time | 77648 seconds = 21 h 34 min 8 s |
Is 77648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77648 ÷ 2 = 38824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77648 ÷ 4 = 19412) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (77648 ÷ 8 = 9706) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77648 a prime number?
No. 77648 = × 23 × 211, so it is divisible by 2.
What are the factors of 77648?
1, 2, 4, 8, 16, 23, 46, 92, 184, 211, 368, 422, 844, 1688, 3376, 4853, 9706, 19412, 38824, 77648.
What is 77648 in binary?
10010111101010000 (hexadecimal 12F50, octal 227520).
What is the square root of 77648?
About 278.6539, exactly 4√4853.
Is 77648 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 77648?
It is a composite number with 20 divisors.