The number 13300
13300 is a composite number with 36 divisors. Its prime factorisation is × × 7 × 19. Divisors (36): 1, 2, 4, 5, 7, 10, 14, 19, 20, 25, 28, 35, 38, 50, 70, 76 … 13300.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13300: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 7.
- 2
13300 is composite. Its prime factorisation is
- 3
The divisors add up to 34720; without 13300 itself that is 21420, so 13300 is abundant (21420 is more than 13300). Euler's totient φ(13300) = 4320 numbers up to 13300 share no factor with it.
- 4
The digits of 13300 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13300 = 2^{2} \times 5^{2} \times 7 \times 19 \]13300 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 34720 |
| Euler totient φ(n) | 4320 |
| Square | 176890000 |
| Cube | 2352637000000 |
| Square root | 115.325626 (= 10√133) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.33 × |
13300 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand three hundred |
| Binary (base 2) | 11001111110100 |
| Octal (base 8) | 31764 |
| Hexadecimal (base 16) | 33F4 |
| Base 3 | 200020121 |
| As time | 13300 seconds = 3 h 41 min 40 s |
Is 13300 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13300 ÷ 2 = 6650) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13300 ÷ 4 = 3325) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13300 ÷ 5 = 2660) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13300 ÷ 7 = 1900) | 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 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13300 ÷ 10 = 1330) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13300 a prime number?
No. 13300 = × × 7 × 19, so it is divisible by 2.
What are the factors of 13300?
1, 2, 4, 5, 7, 10, 14, 19, 20, 25, 28, 35, 38, 50, 70, 76, 95, 100, 133, 140, 175, 190, 266, 350, 380, 475, 532, 665, 700, 950, 1330, 1900, 2660, 3325, 6650, 13300.
What is 13300 in binary?
11001111110100 (hexadecimal 33F4, octal 31764).
What is the square root of 13300?
About 115.3256, exactly 10√133.
Is 13300 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 13300?
13300 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 7.