The number 13764
13764 is a composite number with 24 divisors. Its prime factorisation is × 3 × 31 × 37. Divisors (24): 1, 2, 3, 4, 6, 12, 31, 37, 62, 74, 93, 111, 124, 148, 186, 222 … 13764.
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How to work it out
- 1
13764 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13764 is composite. Its prime factorisation is
- 3
The divisors add up to 34048; without 13764 itself that is 20284, so 13764 is abundant (20284 is more than 13764). Euler's totient φ(13764) = 4320 numbers up to 13764 share no factor with it.
- 4
The digits of 13764 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13764 = 2^{2} \times 3 \times 31 \times 37 \]13764 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 34048 |
| Euler totient φ(n) | 4320 |
| Square | 189447696 |
| Cube | 2607558087744 |
| Square root | 117.320075 (= 2√3441) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3764 × |
13764 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and sixty-four |
| Binary (base 2) | 11010111000100 |
| Octal (base 8) | 32704 |
| Hexadecimal (base 16) | 35C4 |
| Base 3 | 200212210 |
| As time | 13764 seconds = 3 h 49 min 24 s |
Is 13764 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13764 ÷ 2 = 6882) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13764 ÷ 3 = 4588) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13764 ÷ 4 = 3441) | 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 (13764 ÷ 6 = 2294) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 3) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13764 ÷ 12 = 1147) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13764 a prime number?
No. 13764 = × 3 × 31 × 37, so it is divisible by 2.
What are the factors of 13764?
1, 2, 3, 4, 6, 12, 31, 37, 62, 74, 93, 111, 124, 148, 186, 222, 372, 444, 1147, 2294, 3441, 4588, 6882, 13764.
What is 13764 in binary?
11010111000100 (hexadecimal 35C4, octal 32704).
What is the square root of 13764?
About 117.3201, exactly 2√3441.
Is 13764 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13764?
It is a composite number with 24 divisors.