The number 13776
13776 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 41. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 41, 42, 48 … 13776.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13776: a Harshad number: divisible by its digit sum 24.
- 2
13776 is composite. Its prime factorisation is
- 3
The divisors add up to 41664; without 13776 itself that is 27888, so 13776 is abundant (27888 is more than 13776). Euler's totient φ(13776) = 3840 numbers up to 13776 share no factor with it.
- 4
The digits of 13776 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13776 = 2^{4} \times 3 \times 7 \times 41 \]13776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 41664 |
| Euler totient φ(n) | 3840 |
| Square | 189778176 |
| Cube | 2614384152576 |
| Square root | 117.371206 (= 4√861) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3776 × |
13776 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and seventy-six |
| Binary (base 2) | 11010111010000 |
| Octal (base 8) | 32720 |
| Hexadecimal (base 16) | 35D0 |
| Base 3 | 200220020 |
| As time | 13776 seconds = 3 h 49 min 36 s |
Is 13776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13776 ÷ 2 = 6888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13776 ÷ 3 = 4592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13776 ÷ 4 = 3444) | 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 (13776 ÷ 6 = 2296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13776 ÷ 7 = 1968) | 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 (13776 ÷ 8 = 1722) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13776 ÷ 12 = 1148) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13776 a prime number?
No. 13776 = × 3 × 7 × 41, so it is divisible by 2.
What are the factors of 13776?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 41, 42, 48, 56, 82, 84, 112, 123, 164, 168, 246, 287, 328, 336, 492, 574, 656, 861, 984, 1148, 1722, 1968, 2296, 3444, 4592, 6888, 13776.
What is 13776 in binary?
11010111010000 (hexadecimal 35D0, octal 32720).
What is the square root of 13776?
About 117.3712, exactly 4√861.
Is 13776 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 13776?
13776 is a Harshad number: divisible by its digit sum 24.