The number 13754
13754 is a composite number with 12 divisors. Its prime factorisation is 2 × 13 × . Divisors (12): 1, 2, 13, 23, 26, 46, 299, 529, 598, 1058, 6877, 13754.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13754: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13754 is composite. Its prime factorisation is
- 3
The divisors add up to 23226; without 13754 itself that is 9472, so 13754 is deficient (9472 is less than 13754). Euler's totient φ(13754) = 6072 numbers up to 13754 share no factor with it.
- 4
The digits of 13754 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13754 = 2 \times 13 \times 23^{2} \]13754 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 23226 |
| Euler totient φ(n) | 6072 |
| Square | 189172516 |
| Cube | 2601878785064 |
| Square root | 117.277449 (= 23√26) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3754 × |
13754 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and fifty-four |
| Binary (base 2) | 11010110111010 |
| Octal (base 8) | 32672 |
| Hexadecimal (base 16) | 35BA |
| Base 3 | 200212102 |
| As time | 13754 seconds = 3 h 49 min 14 s |
Is 13754 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13754 ÷ 2 = 6877) | 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 | No (remainder 2) | 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 6) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13754 a prime number?
No. 13754 = 2 × 13 × , so it is divisible by 2.
What are the factors of 13754?
1, 2, 13, 23, 26, 46, 299, 529, 598, 1058, 6877, 13754.
What is 13754 in binary?
11010110111010 (hexadecimal 35BA, octal 32672).
What is the square root of 13754?
About 117.2774, exactly 23√26.
Is 13754 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 13754?
13754 is a happy number: repeatedly adding the squares of its digits reaches 1.