The number 13748
13748 is a composite number with 12 divisors. Its prime factorisation is × 7 × 491. Divisors (12): 1, 2, 4, 7, 14, 28, 491, 982, 1964, 3437, 6874, 13748.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13748: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13748 is composite. Its prime factorisation is
- 3
The divisors add up to 27552; without 13748 itself that is 13804, so 13748 is abundant (13804 is more than 13748). Euler's totient φ(13748) = 5880 numbers up to 13748 share no factor with it.
- 4
The digits of 13748 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 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13748 = 2^{2} \times 7 \times 491 \]13748 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 27552 |
| Euler totient φ(n) | 5880 |
| Square | 189007504 |
| Cube | 2598475164992 |
| Square root | 117.251866 (= 2√3437) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3748 × |
13748 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and forty-eight |
| Binary (base 2) | 11010110110100 |
| Octal (base 8) | 32664 |
| Hexadecimal (base 16) | 35B4 |
| Base 3 | 200212012 |
| As time | 13748 seconds = 3 h 49 min 8 s |
Is 13748 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13748 ÷ 2 = 6874) | 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 (13748 ÷ 4 = 3437) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | Yes (13748 ÷ 7 = 1964) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 13748 a prime number?
No. 13748 = × 7 × 491, so it is divisible by 2.
What are the factors of 13748?
1, 2, 4, 7, 14, 28, 491, 982, 1964, 3437, 6874, 13748.
What is 13748 in binary?
11010110110100 (hexadecimal 35B4, octal 32664).
What is the square root of 13748?
About 117.2519, exactly 2√3437.
Is 13748 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 13748?
13748 is a happy number: repeatedly adding the squares of its digits reaches 1.