The number 13540
13540 is a composite number with 12 divisors. Its prime factorisation is × 5 × 677. Divisors (12): 1, 2, 4, 5, 10, 20, 677, 1354, 2708, 3385, 6770, 13540.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13540 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13540 is composite. Its prime factorisation is
- 3
The divisors add up to 28476; without 13540 itself that is 14936, so 13540 is abundant (14936 is more than 13540). Euler's totient φ(13540) = 5408 numbers up to 13540 share no factor with it.
- 4
The digits of 13540 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 182 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13540 = 2^{2} \times 5 \times 677 \]13540 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 28476 |
| Euler totient φ(n) | 5408 |
| Square | 183331600 |
| Cube | 2482309864000 |
| Square root | 116.361506 (= 2√3385) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 182 |
| Scientific notation | 1.354 × |
13540 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and forty |
| Binary (base 2) | 11010011100100 |
| Octal (base 8) | 32344 |
| Hexadecimal (base 16) | 34E4 |
| Base 3 | 200120111 |
| As time | 13540 seconds = 3 h 45 min 40 s |
Is 13540 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13540 ÷ 2 = 6770) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13540 ÷ 4 = 3385) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13540 ÷ 5 = 2708) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13540 ÷ 10 = 1354) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13540 a prime number?
No. 13540 = × 5 × 677, so it is divisible by 2.
What are the factors of 13540?
1, 2, 4, 5, 10, 20, 677, 1354, 2708, 3385, 6770, 13540.
What is 13540 in binary?
11010011100100 (hexadecimal 34E4, octal 32344).
What is the square root of 13540?
About 116.3615, exactly 2√3385.
Is 13540 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 13540?
It is a composite number with 12 divisors.