The number 77216
77216 is a composite number with 24 divisors. Its prime factorisation is × 19 × 127. Divisors (24): 1, 2, 4, 8, 16, 19, 32, 38, 76, 127, 152, 254, 304, 508, 608, 1016 … 77216.
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How to work it out
- 1
What is special about 77216: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77216 is composite. Its prime factorisation is
- 3
The divisors add up to 161280; without 77216 itself that is 84064, so 77216 is abundant (84064 is more than 77216). Euler's totient φ(77216) = 36288 numbers up to 77216 share no factor with it.
- 4
The digits of 77216 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77216 = 2^{5} \times 19 \times 127 \]77216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 161280 |
| Euler totient φ(n) | 36288 |
| Square | 5962310656 |
| Cube | 460385779613696 |
| Square root | 277.877671 (= 4√4826) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.7216 × |
77216 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand two hundred and sixteen |
| Binary (base 2) | 10010110110100000 |
| Octal (base 8) | 226640 |
| Hexadecimal (base 16) | 12DA0 |
| Base 3 | 10220220212 |
| As time | 77216 seconds = 21 h 26 min 56 s |
Is 77216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77216 ÷ 2 = 38608) | 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 (77216 ÷ 4 = 19304) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 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 (77216 ÷ 8 = 9652) | 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 6) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77216 a prime number?
No. 77216 = × 19 × 127, so it is divisible by 2.
What are the factors of 77216?
1, 2, 4, 8, 16, 19, 32, 38, 76, 127, 152, 254, 304, 508, 608, 1016, 2032, 2413, 4064, 4826, 9652, 19304, 38608, 77216.
What is 77216 in binary?
10010110110100000 (hexadecimal 12DA0, octal 226640).
What is the square root of 77216?
About 277.8777, exactly 4√4826.
Is 77216 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 77216?
77216 is a happy number: repeatedly adding the squares of its digits reaches 1.