The number 77712
77712 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1619. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1619, 3238, 4857, 6476, 9714, 12952 … 77712.
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How to work it out
- 1
What is special about 77712: a Harshad number: divisible by its digit sum 24.
- 2
77712 is composite. Its prime factorisation is
- 3
The divisors add up to 200880; without 77712 itself that is 123168, so 77712 is abundant (123168 is more than 77712). Euler's totient φ(77712) = 25888 numbers up to 77712 share no factor with it.
- 4
The digits of 77712 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77712 = 2^{4} \times 3 \times 1619 \]77712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 200880 |
| Euler totient φ(n) | 25888 |
| Square | 6039154944 |
| Cube | 469314809008128 |
| Square root | 278.768721 (= 4√4857) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.7712 × |
77712 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and twelve |
| Binary (base 2) | 10010111110010000 |
| Octal (base 8) | 227620 |
| Hexadecimal (base 16) | 12F90 |
| Base 3 | 10221121020 |
| As time | 77712 seconds = 21 h 35 min 12 s |
Is 77712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77712 ÷ 2 = 38856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77712 ÷ 3 = 25904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77712 ÷ 4 = 19428) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77712 ÷ 6 = 12952) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (77712 ÷ 8 = 9714) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77712 ÷ 12 = 6476) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77712 a prime number?
No. 77712 = × 3 × 1619, so it is divisible by 2.
What are the factors of 77712?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1619, 3238, 4857, 6476, 9714, 12952, 19428, 25904, 38856, 77712.
What is 77712 in binary?
10010111110010000 (hexadecimal 12F90, octal 227620).
What is the square root of 77712?
About 278.7687, exactly 4√4857.
Is 77712 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77712?
77712 is a Harshad number: divisible by its digit sum 24.