The number 13524
13524 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 23. Divisors (36): 1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 49, 69, 84 … 13524.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13524 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13524 is composite. Its prime factorisation is
- 3
The divisors add up to 38304; without 13524 itself that is 24780, so 13524 is abundant (24780 is more than 13524). Euler's totient φ(13524) = 3696 numbers up to 13524 share no factor with it.
- 4
The digits of 13524 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13524 = 2^{2} \times 3 \times 7^{2} \times 23 \]13524 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 38304 |
| Euler totient φ(n) | 3696 |
| Square | 182898576 |
| Cube | 2473520341824 |
| Square root | 116.292734 (= 14√69) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3524 × |
13524 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and twenty-four |
| Binary (base 2) | 11010011010100 |
| Octal (base 8) | 32324 |
| Hexadecimal (base 16) | 34D4 |
| Base 3 | 200112220 |
| As time | 13524 seconds = 3 h 45 min 24 s |
Is 13524 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13524 ÷ 2 = 6762) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13524 ÷ 3 = 4508) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13524 ÷ 4 = 3381) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13524 ÷ 6 = 2254) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13524 ÷ 7 = 1932) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (13524 ÷ 12 = 1127) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13524 a prime number?
No. 13524 = × 3 × × 23, so it is divisible by 2.
What are the factors of 13524?
1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 49, 69, 84, 92, 98, 138, 147, 161, 196, 276, 294, 322, 483, 588, 644, 966, 1127, 1932, 2254, 3381, 4508, 6762, 13524.
What is 13524 in binary?
11010011010100 (hexadecimal 34D4, octal 32324).
What is the square root of 13524?
About 116.2927, exactly 14√69.
Is 13524 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13524?
It is a composite number with 36 divisors.