The number 13580
13580 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 97. Divisors (24): 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 97, 140, 194, 388, 485 … 13580.
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How to work it out
- 1
13580 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13580 is composite. Its prime factorisation is
- 3
The divisors add up to 32928; without 13580 itself that is 19348, so 13580 is abundant (19348 is more than 13580). Euler's totient φ(13580) = 4608 numbers up to 13580 share no factor with it.
- 4
The digits of 13580 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13580 = 2^{2} \times 5 \times 7 \times 97 \]13580 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 32928 |
| Euler totient φ(n) | 4608 |
| Square | 184416400 |
| Cube | 2504374712000 |
| Square root | 116.533257 (= 2√3395) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.358 × |
13580 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and eighty |
| Binary (base 2) | 11010100001100 |
| Octal (base 8) | 32414 |
| Hexadecimal (base 16) | 350C |
| Base 3 | 200121222 |
| As time | 13580 seconds = 3 h 46 min 20 s |
Is 13580 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13580 ÷ 2 = 6790) | 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 (13580 ÷ 4 = 3395) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13580 ÷ 5 = 2716) | 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 (13580 ÷ 7 = 1940) | 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13580 ÷ 10 = 1358) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13580 a prime number?
No. 13580 = × 5 × 7 × 97, so it is divisible by 2.
What are the factors of 13580?
1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 97, 140, 194, 388, 485, 679, 970, 1358, 1940, 2716, 3395, 6790, 13580.
What is 13580 in binary?
11010100001100 (hexadecimal 350C, octal 32414).
What is the square root of 13580?
About 116.5333, exactly 2√3395.
Is 13580 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13580?
It is a composite number with 24 divisors.