The number 31776
31776 is a composite number with 24 divisors. Its prime factorisation is × 3 × 331. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 331, 662, 993, 1324 … 31776.
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How to work it out
- 1
What is special about 31776: a Harshad number: divisible by its digit sum 24.
- 2
31776 is composite. Its prime factorisation is
- 3
The divisors add up to 83664; without 31776 itself that is 51888, so 31776 is abundant (51888 is more than 31776). Euler's totient φ(31776) = 10560 numbers up to 31776 share no factor with it.
- 4
The digits of 31776 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 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31776 = 2^{5} \times 3 \times 331 \]31776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 83664 |
| Euler totient φ(n) | 10560 |
| Square | 1009714176 |
| Cube | 32084677656576 |
| Square root | 178.258240 (= 4√1986) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.1776 × |
31776 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand seven hundred and seventy-six |
| Binary (base 2) | 111110000100000 |
| Octal (base 8) | 76040 |
| Hexadecimal (base 16) | 7C20 |
| Base 3 | 1121120220 |
| As time | 31776 seconds = 8 h 49 min 36 s |
Is 31776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31776 ÷ 2 = 15888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31776 ÷ 3 = 10592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31776 ÷ 4 = 7944) | 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 (31776 ÷ 6 = 5296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (31776 ÷ 8 = 3972) | 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 6) | 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 (31776 ÷ 12 = 2648) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31776 a prime number?
No. 31776 = × 3 × 331, so it is divisible by 2.
What are the factors of 31776?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 331, 662, 993, 1324, 1986, 2648, 3972, 5296, 7944, 10592, 15888, 31776.
What is 31776 in binary?
111110000100000 (hexadecimal 7C20, octal 76040).
What is the square root of 31776?
About 178.2582, exactly 4√1986.
Is 31776 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 31776?
31776 is a Harshad number: divisible by its digit sum 24.