The number 77736
77736 is a composite number with 32 divisors. Its prime factorisation is × 3 × 41 × 79. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 24, 41, 79, 82, 123, 158, 164, 237, 246 … 77736.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77736: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77736 is composite. Its prime factorisation is
- 3
The divisors add up to 201600; without 77736 itself that is 123864, so 77736 is abundant (123864 is more than 77736). Euler's totient φ(77736) = 24960 numbers up to 77736 share no factor with it.
- 4
The digits of 77736 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77736 = 2^{3} \times 3 \times 41 \times 79 \]77736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 201600 |
| Euler totient φ(n) | 24960 |
| Square | 6042885696 |
| Cube | 469749762464256 |
| Square root | 278.811764 (= 2√19434) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7736 × |
77736 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and thirty-six |
| Binary (base 2) | 10010111110101000 |
| Octal (base 8) | 227650 |
| Hexadecimal (base 16) | 12FA8 |
| Base 3 | 10221122010 |
| As time | 77736 seconds = 21 h 35 min 36 s |
Is 77736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77736 ÷ 2 = 38868) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77736 ÷ 3 = 25912) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77736 ÷ 4 = 19434) | 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 | Yes (77736 ÷ 6 = 12956) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (77736 ÷ 8 = 9717) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77736 ÷ 12 = 6478) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77736 a prime number?
No. 77736 = × 3 × 41 × 79, so it is divisible by 2.
What are the factors of 77736?
1, 2, 3, 4, 6, 8, 12, 24, 41, 79, 82, 123, 158, 164, 237, 246, 316, 328, 474, 492, 632, 948, 984, 1896, 3239, 6478, 9717, 12956, 19434, 25912, 38868, 77736.
What is 77736 in binary?
10010111110101000 (hexadecimal 12FA8, octal 227650).
What is the square root of 77736?
About 278.8118, exactly 2√19434.
Is 77736 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77736?
77736 is a happy number: repeatedly adding the squares of its digits reaches 1.