The number 13200
13200 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 11. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25 … 13200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13200: a Harshad number: divisible by its digit sum 6.
- 2
13200 is composite. Its prime factorisation is
- 3
The divisors add up to 46128; without 13200 itself that is 32928, so 13200 is abundant (32928 is more than 13200). Euler's totient φ(13200) = 3200 numbers up to 13200 share no factor with it.
- 4
The digits of 13200 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13200 = 2^{4} \times 3 \times 5^{2} \times 11 \]13200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 46128 |
| Euler totient φ(n) | 3200 |
| Square | 174240000 |
| Cube | 2299968000000 |
| Square root | 114.891253 (= 20√33) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.32 × |
13200 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand two hundred |
| Binary (base 2) | 11001110010000 |
| Octal (base 8) | 31620 |
| Hexadecimal (base 16) | 3390 |
| Base 3 | 200002220 |
| As time | 13200 seconds = 3 h 40 min 0 s |
Is 13200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13200 ÷ 2 = 6600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13200 ÷ 3 = 4400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13200 ÷ 4 = 3300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13200 ÷ 5 = 2640) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13200 ÷ 6 = 2200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (13200 ÷ 8 = 1650) | 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 | Yes (13200 ÷ 10 = 1320) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13200 ÷ 11 = 1200) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13200 ÷ 12 = 1100) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13200 a prime number?
No. 13200 = × 3 × × 11, so it is divisible by 2.
What are the factors of 13200?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 132, 150, 165, 176, 200, 220, 240, 264, 275, 300, 330, 400, 440, 528, 550, 600, 660, 825, 880, 1100, 1200, 1320, 1650, 2200, 2640, 3300, 4400, 6600, 13200.
What is 13200 in binary?
11001110010000 (hexadecimal 3390, octal 31620).
What is the square root of 13200?
About 114.8913, exactly 20√33.
Is 13200 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 13200?
13200 is a Harshad number: divisible by its digit sum 6.