The number 13800
13800 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 23. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40 … 13800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13800: a Harshad number: divisible by its digit sum 12.
- 2
13800 is composite. Its prime factorisation is
- 3
The divisors add up to 44640; without 13800 itself that is 30840, so 13800 is abundant (30840 is more than 13800). Euler's totient φ(13800) = 3520 numbers up to 13800 share no factor with it.
- 4
The digits of 13800 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13800 = 2^{3} \times 3 \times 5^{2} \times 23 \]13800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 44640 |
| Euler totient φ(n) | 3520 |
| Square | 190440000 |
| Cube | 2628072000000 |
| Square root | 117.473401 (= 10√138) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.38 × |
13800 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred |
| Binary (base 2) | 11010111101000 |
| Octal (base 8) | 32750 |
| Hexadecimal (base 16) | 35E8 |
| Base 3 | 200221010 |
| As time | 13800 seconds = 3 h 50 min 0 s |
Is 13800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13800 ÷ 2 = 6900) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13800 ÷ 3 = 4600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13800 ÷ 4 = 3450) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13800 ÷ 5 = 2760) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13800 ÷ 6 = 2300) | 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 | Yes (13800 ÷ 8 = 1725) | 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 (13800 ÷ 10 = 1380) | 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 | Yes (13800 ÷ 12 = 1150) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13800 a prime number?
No. 13800 = × 3 × × 23, so it is divisible by 2.
What are the factors of 13800?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40, 46, 50, 60, 69, 75, 92, 100, 115, 120, 138, 150, 184, 200, 230, 276, 300, 345, 460, 552, 575, 600, 690, 920, 1150, 1380, 1725, 2300, 2760, 3450, 4600, 6900, 13800.
What is 13800 in binary?
11010111101000 (hexadecimal 35E8, octal 32750).
What is the square root of 13800?
About 117.4734, exactly 10√138.
Is 13800 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13800?
13800 is a Harshad number: divisible by its digit sum 12.