The number 10731
10731 is a triangular number: 1 + 2 + … + 146 = 10731. Its prime factorisation is 3 × × 73. Divisors (12): 1, 3, 7, 21, 49, 73, 147, 219, 511, 1533, 3577, 10731.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10731: a triangular number: 1 + 2 + … + 146 = 10731.
- 2
10731 is composite. Its prime factorisation is
- 3
The divisors add up to 16872; without 10731 itself that is 6141, so 10731 is deficient (6141 is less than 10731). Euler's totient φ(10731) = 6048 numbers up to 10731 share no factor with it.
- 4
The digits of 10731 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10731 = 3 \times 7^{2} \times 73 \]10731 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16872 |
| Euler totient φ(n) | 6048 |
| Square | 115154361 |
| Cube | 1235721447891 |
| Square root | 103.590540 (= 7√219) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 47 |
| Scientific notation | 1.0731 × |
10731 in other forms
| Form | Value |
|---|---|
| In words | ten thousand seven hundred and thirty-one |
| Binary (base 2) | 10100111101011 |
| Octal (base 8) | 24753 |
| Hexadecimal (base 16) | 29EB |
| Base 3 | 112201110 |
| As time | 10731 seconds = 2 h 58 min 51 s |
Is 10731 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10731 ÷ 3 = 3577) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10731 ÷ 7 = 1533) | 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 | No (remainder 3) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10731 a prime number?
No. 10731 = 3 × × 73, so it is divisible by 3.
What are the factors of 10731?
1, 3, 7, 21, 49, 73, 147, 219, 511, 1533, 3577, 10731.
What is 10731 in binary?
10100111101011 (hexadecimal 29EB, octal 24753).
What is the square root of 10731?
About 103.5905, exactly 7√219.
Is 10731 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10731?
10731 is a triangular number: 1 + 2 + … + 146 = 10731.