The number 13530
13530 is a triangular number: 1 + 2 + … + 164 = 13530. Its prime factorisation is 2 × 3 × 5 × 11 × 41. Divisors (32): 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 41, 55, 66, 82, 110 … 13530.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13530: a triangular number: 1 + 2 + … + 164 = 13530; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13530 is composite. Its prime factorisation is
- 3
The divisors add up to 36288; without 13530 itself that is 22758, so 13530 is abundant (22758 is more than 13530). Euler's totient φ(13530) = 3200 numbers up to 13530 share no factor with it.
- 4
The digits of 13530 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13530 = 2 \times 3 \times 5 \times 11 \times 41 \]
13530 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 36288 |
| Euler totient φ(n) | 3200 |
| Square | 183060900 |
| Cube | 2476813977000 |
| Square root | 116.318528 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.353 × |
13530 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and thirty |
| Binary (base 2) | 11010011011010 |
| Octal (base 8) | 32332 |
| Hexadecimal (base 16) | 34DA |
| Base 3 | 200120010 |
| As time | 13530 seconds = 3 h 45 min 30 s |
Is 13530 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13530 ÷ 2 = 6765) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13530 ÷ 3 = 4510) | 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 (13530 ÷ 5 = 2706) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13530 ÷ 6 = 2255) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13530 ÷ 10 = 1353) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13530 ÷ 11 = 1230) | 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 13530 a prime number?
No. 13530 = 2 × 3 × 5 × 11 × 41, so it is divisible by 2.
What are the factors of 13530?
1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 41, 55, 66, 82, 110, 123, 165, 205, 246, 330, 410, 451, 615, 902, 1230, 1353, 2255, 2706, 4510, 6765, 13530.
What is 13530 in binary?
11010011011010 (hexadecimal 34DA, octal 32332).
What is the square root of 13530?
About 116.3185.
Is 13530 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13530?
13530 is a triangular number: 1 + 2 + … + 164 = 13530; a happy number: repeatedly adding the squares of its digits reaches 1.