The number 13590
13590 is a composite number with 24 divisors. Its prime factorisation is 2 × × 5 × 151. Divisors (24): 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 151, 302, 453, 755 … 13590.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13590: a Harshad number: divisible by its digit sum 18.
- 2
13590 is composite. Its prime factorisation is
- 3
The divisors add up to 35568; without 13590 itself that is 21978, so 13590 is abundant (21978 is more than 13590). Euler's totient φ(13590) = 3600 numbers up to 13590 share no factor with it.
- 4
The digits of 13590 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13590 = 2 \times 3^{2} \times 5 \times 151 \]13590 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 35568 |
| Euler totient φ(n) | 3600 |
| Square | 184688100 |
| Cube | 2509911279000 |
| Square root | 116.576155 (= 3√1510) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.359 × |
13590 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and ninety |
| Binary (base 2) | 11010100010110 |
| Octal (base 8) | 32426 |
| Hexadecimal (base 16) | 3516 |
| Base 3 | 200122100 |
| As time | 13590 seconds = 3 h 46 min 30 s |
Is 13590 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13590 ÷ 2 = 6795) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13590 ÷ 3 = 4530) | 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 | Yes (13590 ÷ 5 = 2718) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13590 ÷ 6 = 2265) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (13590 ÷ 9 = 1510) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13590 ÷ 10 = 1359) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | 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 13590 a prime number?
No. 13590 = 2 × × 5 × 151, so it is divisible by 2.
What are the factors of 13590?
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 151, 302, 453, 755, 906, 1359, 1510, 2265, 2718, 4530, 6795, 13590.
What is 13590 in binary?
11010100010110 (hexadecimal 3516, octal 32426).
What is the square root of 13590?
About 116.5762, exactly 3√1510.
Is 13590 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13590?
13590 is a Harshad number: divisible by its digit sum 18.