The number 13734
13734 is a composite number with 24 divisors. Its prime factorisation is 2 × × 7 × 109. Divisors (24): 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 109, 126, 218, 327, 654 … 13734.
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How to work it out
- 1
What is special about 13734: a Harshad number: divisible by its digit sum 18.
- 2
13734 is composite. Its prime factorisation is
- 3
The divisors add up to 34320; without 13734 itself that is 20586, so 13734 is abundant (20586 is more than 13734). Euler's totient φ(13734) = 3888 numbers up to 13734 share no factor with it.
- 4
The digits of 13734 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13734 = 2 \times 3^{2} \times 7 \times 109 \]13734 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 34320 |
| Euler totient φ(n) | 3888 |
| Square | 188622756 |
| Cube | 2590544930904 |
| Square root | 117.192150 (= 3√1526) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3734 × |
13734 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and thirty-four |
| Binary (base 2) | 11010110100110 |
| Octal (base 8) | 32646 |
| Hexadecimal (base 16) | 35A6 |
| Base 3 | 200211200 |
| As time | 13734 seconds = 3 h 48 min 54 s |
Is 13734 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13734 ÷ 2 = 6867) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13734 ÷ 3 = 4578) | 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 | Yes (13734 ÷ 6 = 2289) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13734 ÷ 7 = 1962) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13734 ÷ 9 = 1526) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13734 a prime number?
No. 13734 = 2 × × 7 × 109, so it is divisible by 2.
What are the factors of 13734?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 109, 126, 218, 327, 654, 763, 981, 1526, 1962, 2289, 4578, 6867, 13734.
What is 13734 in binary?
11010110100110 (hexadecimal 35A6, octal 32646).
What is the square root of 13734?
About 117.1921, exactly 3√1526.
Is 13734 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13734?
13734 is a Harshad number: divisible by its digit sum 18.