The number 13640
13640 is a composite number with 32 divisors. Its prime factorisation is × 5 × 11 × 31. Divisors (32): 1, 2, 4, 5, 8, 10, 11, 20, 22, 31, 40, 44, 55, 62, 88, 110 … 13640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13640 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13640 is composite. Its prime factorisation is
- 3
The divisors add up to 34560; without 13640 itself that is 20920, so 13640 is abundant (20920 is more than 13640). Euler's totient φ(13640) = 4800 numbers up to 13640 share no factor with it.
- 4
The digits of 13640 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13640 = 2^{3} \times 5 \times 11 \times 31 \]13640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 34560 |
| Euler totient φ(n) | 4800 |
| Square | 186049600 |
| Cube | 2537716544000 |
| Square root | 116.790411 (= 2√3410) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.364 × |
13640 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and forty |
| Binary (base 2) | 11010101001000 |
| Octal (base 8) | 32510 |
| Hexadecimal (base 16) | 3548 |
| Base 3 | 200201012 |
| As time | 13640 seconds = 3 h 47 min 20 s |
Is 13640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13640 ÷ 2 = 6820) | 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 (13640 ÷ 4 = 3410) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13640 ÷ 5 = 2728) | 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 4) | 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 | Yes (13640 ÷ 8 = 1705) | 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 | Yes (13640 ÷ 10 = 1364) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13640 ÷ 11 = 1240) | 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 13640 a prime number?
No. 13640 = × 5 × 11 × 31, so it is divisible by 2.
What are the factors of 13640?
1, 2, 4, 5, 8, 10, 11, 20, 22, 31, 40, 44, 55, 62, 88, 110, 124, 155, 220, 248, 310, 341, 440, 620, 682, 1240, 1364, 1705, 2728, 3410, 6820, 13640.
What is 13640 in binary?
11010101001000 (hexadecimal 3548, octal 32510).
What is the square root of 13640?
About 116.7904, exactly 2√3410.
Is 13640 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 13640?
It is a composite number with 32 divisors.