The number 10764
10764 is a composite number with 36 divisors. Its prime factorisation is × × 13 × 23. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 13, 18, 23, 26, 36, 39, 46, 52, 69 … 10764.
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How to work it out
- 1
What is special about 10764: a Harshad number: divisible by its digit sum 18.
- 2
10764 is composite. Its prime factorisation is
- 3
The divisors add up to 30576; without 10764 itself that is 19812, so 10764 is abundant (19812 is more than 10764). Euler's totient φ(10764) = 3168 numbers up to 10764 share no factor with it.
- 4
The digits of 10764 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 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10764 = 2^{2} \times 3^{2} \times 13 \times 23 \]10764 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 30576 |
| Euler totient φ(n) | 3168 |
| Square | 115863696 |
| Cube | 1247156823744 |
| Square root | 103.749699 (= 6√299) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.0764 × |
10764 in other forms
| Form | Value |
|---|---|
| In words | ten thousand seven hundred and sixty-four |
| Binary (base 2) | 10101000001100 |
| Octal (base 8) | 25014 |
| Hexadecimal (base 16) | 2A0C |
| Base 3 | 112202200 |
| As time | 10764 seconds = 2 h 59 min 24 s |
Is 10764 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10764 ÷ 2 = 5382) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10764 ÷ 3 = 3588) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10764 ÷ 4 = 2691) | 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 | Yes (10764 ÷ 6 = 1794) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10764 ÷ 9 = 1196) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10764 ÷ 12 = 897) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10764 a prime number?
No. 10764 = × × 13 × 23, so it is divisible by 2.
What are the factors of 10764?
1, 2, 3, 4, 6, 9, 12, 13, 18, 23, 26, 36, 39, 46, 52, 69, 78, 92, 117, 138, 156, 207, 234, 276, 299, 414, 468, 598, 828, 897, 1196, 1794, 2691, 3588, 5382, 10764.
What is 10764 in binary?
10101000001100 (hexadecimal 2A0C, octal 25014).
What is the square root of 10764?
About 103.7497, exactly 6√299.
Is 10764 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 10764?
10764 is a Harshad number: divisible by its digit sum 18.