The number 13500
13500 is a composite number with 48 divisors. Its prime factorisation is × × . Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36 … 13500.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13500: a Harshad number: divisible by its digit sum 9.
- 2
13500 is composite. Its prime factorisation is
- 3
The divisors add up to 43680; without 13500 itself that is 30180, so 13500 is abundant (30180 is more than 13500). Euler's totient φ(13500) = 3600 numbers up to 13500 share no factor with it.
- 4
The digits of 13500 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13500 = 2^{2} \times 3^{3} \times 5^{3} \]13500 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 43680 |
| Euler totient φ(n) | 3600 |
| Square | 182250000 |
| Cube | 2460375000000 |
| Square root | 116.189500 (= 30√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.35 × |
13500 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred |
| Binary (base 2) | 11010010111100 |
| Octal (base 8) | 32274 |
| Hexadecimal (base 16) | 34BC |
| Base 3 | 200112000 |
| As time | 13500 seconds = 3 h 45 min 0 s |
Is 13500 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13500 ÷ 2 = 6750) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13500 ÷ 3 = 4500) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13500 ÷ 4 = 3375) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13500 ÷ 5 = 2700) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13500 ÷ 6 = 2250) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13500 ÷ 9 = 1500) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13500 ÷ 10 = 1350) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13500 ÷ 12 = 1125) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13500 a prime number?
No. 13500 = × × , so it is divisible by 2.
What are the factors of 13500?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 675, 750, 900, 1125, 1350, 1500, 2250, 2700, 3375, 4500, 6750, 13500.
What is 13500 in binary?
11010010111100 (hexadecimal 34BC, octal 32274).
What is the square root of 13500?
About 116.1895, exactly 30√15.
Is 13500 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13500?
13500 is a Harshad number: divisible by its digit sum 9.