The number 13740
13740 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 229. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 229, 458, 687, 916 … 13740.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13740: a Harshad number: divisible by its digit sum 15.
- 2
13740 is composite. Its prime factorisation is
- 3
The divisors add up to 38640; without 13740 itself that is 24900, so 13740 is abundant (24900 is more than 13740). Euler's totient φ(13740) = 3648 numbers up to 13740 share no factor with it.
- 4
The digits of 13740 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13740 = 2^{2} \times 3 \times 5 \times 229 \]13740 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 38640 |
| Euler totient φ(n) | 3648 |
| Square | 188787600 |
| Cube | 2593941624000 |
| Square root | 117.217746 (= 2√3435) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.374 × |
13740 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and forty |
| Binary (base 2) | 11010110101100 |
| Octal (base 8) | 32654 |
| Hexadecimal (base 16) | 35AC |
| Base 3 | 200211220 |
| As time | 13740 seconds = 3 h 49 min 0 s |
Is 13740 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13740 ÷ 2 = 6870) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13740 ÷ 3 = 4580) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13740 ÷ 4 = 3435) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13740 ÷ 5 = 2748) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13740 ÷ 6 = 2290) | 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 4) | 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 | Yes (13740 ÷ 10 = 1374) | 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 | Yes (13740 ÷ 12 = 1145) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13740 a prime number?
No. 13740 = × 3 × 5 × 229, so it is divisible by 2.
What are the factors of 13740?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 229, 458, 687, 916, 1145, 1374, 2290, 2748, 3435, 4580, 6870, 13740.
What is 13740 in binary?
11010110101100 (hexadecimal 35AC, octal 32654).
What is the square root of 13740?
About 117.2177, exactly 2√3435.
Is 13740 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13740?
13740 is a Harshad number: divisible by its digit sum 15.