The number 10724
10724 is a composite number with 12 divisors. Its prime factorisation is × 7 × 383. Divisors (12): 1, 2, 4, 7, 14, 28, 383, 766, 1532, 2681, 5362, 10724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10724: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.
- 2
10724 is composite. Its prime factorisation is
- 3
The divisors add up to 21504; without 10724 itself that is 10780, so 10724 is abundant (10780 is more than 10724). Euler's totient φ(10724) = 4584 numbers up to 10724 share no factor with it.
- 4
The digits of 10724 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10724 = 2^{2} \times 7 \times 383 \]10724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 21504 |
| Euler totient φ(n) | 4584 |
| Square | 115004176 |
| Cube | 1233304783424 |
| Square root | 103.556748 (= 2√2681) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 47 |
| Scientific notation | 1.0724 × |
10724 in other forms
| Form | Value |
|---|---|
| In words | ten thousand seven hundred and twenty-four |
| Binary (base 2) | 10100111100100 |
| Octal (base 8) | 24744 |
| Hexadecimal (base 16) | 29E4 |
| Base 3 | 112201012 |
| As time | 10724 seconds = 2 h 58 min 44 s |
Is 10724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10724 ÷ 2 = 5362) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10724 ÷ 4 = 2681) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10724 ÷ 7 = 1532) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10724 a prime number?
No. 10724 = × 7 × 383, so it is divisible by 2.
What are the factors of 10724?
1, 2, 4, 7, 14, 28, 383, 766, 1532, 2681, 5362, 10724.
What is 10724 in binary?
10100111100100 (hexadecimal 29E4, octal 24744).
What is the square root of 10724?
About 103.5567, exactly 2√2681.
Is 10724 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 10724?
10724 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.