The number 13784
13784 is a composite number with 8 divisors. Its prime factorisation is × 1723. Divisors (8): 1, 2, 4, 8, 1723, 3446, 6892, 13784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13784: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13784 is composite. Its prime factorisation is
- 3
The divisors add up to 25860; without 13784 itself that is 12076, so 13784 is deficient (12076 is less than 13784). Euler's totient φ(13784) = 6888 numbers up to 13784 share no factor with it.
- 4
The digits of 13784 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13784 = 2^{3} \times 1723 \]13784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 25860 |
| Euler totient φ(n) | 6888 |
| Square | 189998656 |
| Cube | 2618941474304 |
| Square root | 117.405281 (= 2√3446) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3784 × |
13784 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and eighty-four |
| Binary (base 2) | 11010111011000 |
| Octal (base 8) | 32730 |
| Hexadecimal (base 16) | 35D8 |
| Base 3 | 200220112 |
| As time | 13784 seconds = 3 h 49 min 44 s |
Is 13784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13784 ÷ 2 = 6892) | 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 (13784 ÷ 4 = 3446) | 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 | No (remainder 1) | 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 (13784 ÷ 8 = 1723) | 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 1) | 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 13784 a prime number?
No. 13784 = × 1723, so it is divisible by 2.
What are the factors of 13784?
1, 2, 4, 8, 1723, 3446, 6892, 13784.
What is 13784 in binary?
11010111011000 (hexadecimal 35D8, octal 32730).
What is the square root of 13784?
About 117.4053, exactly 2√3446.
Is 13784 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 13784?
13784 is a happy number: repeatedly adding the squares of its digits reaches 1.