The number 71712
71712 is a composite number with 48 divisors. Its prime factorisation is × × 83. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 71712.
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How to work it out
- 1
What is special about 71712: a Harshad number: divisible by its digit sum 18.
- 2
71712 is composite. Its prime factorisation is
- 3
The divisors add up to 211680; without 71712 itself that is 139968, so 71712 is abundant (139968 is more than 71712). Euler's totient φ(71712) = 23616 numbers up to 71712 share no factor with it.
- 4
The digits of 71712 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 71712 = 2^{5} \times 3^{3} \times 83 \]71712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 211680 |
| Euler totient φ(n) | 23616 |
| Square | 5142610944 |
| Cube | 368786916016128 |
| Square root | 267.790963 (= 12√498) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.1712 × |
71712 in other forms
| Form | Value |
|---|---|
| In words | seventy-one thousand seven hundred and twelve |
| Binary (base 2) | 10001100000100000 |
| Octal (base 8) | 214040 |
| Hexadecimal (base 16) | 11820 |
| Base 3 | 10122101000 |
| As time | 71712 seconds = 19 h 55 min 12 s |
Is 71712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (71712 ÷ 2 = 35856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (71712 ÷ 3 = 23904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (71712 ÷ 4 = 17928) | 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 (71712 ÷ 6 = 11952) | 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 (71712 ÷ 8 = 8964) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (71712 ÷ 9 = 7968) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (71712 ÷ 12 = 5976) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 71712 a prime number?
No. 71712 = × × 83, so it is divisible by 2.
What are the factors of 71712?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 83, 96, 108, 144, 166, 216, 249, 288, 332, 432, 498, 664, 747, 864, 996, 1328, 1494, 1992, 2241, 2656, 2988, 3984, 4482, 5976, 7968, 8964, 11952, 17928, 23904, 35856, 71712.
What is 71712 in binary?
10001100000100000 (hexadecimal 11820, octal 214040).
What is the square root of 71712?
About 267.7910, exactly 12√498.
Is 71712 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 71712?
71712 is a Harshad number: divisible by its digit sum 18.