The number 300
300 is a triangular number: 1 + 2 + … + 24 = 300. Its prime factorisation is × 3 × . Divisors (18): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 300.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 300: a triangular number: 1 + 2 + … + 24 = 300; a Harshad number: divisible by its digit sum 3.
- 2
300 is composite. Its prime factorisation is
- 3
The divisors add up to 868; without 300 itself that is 568, so 300 is abundant (568 is more than 300). Euler's totient φ(300) = 80 numbers up to 300 share no factor with it.
- 4
The digits of 300 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 16 steps to reach 1.
LaTeX source of the formulas on this page
\[ 300 = 2^{2} \times 3 \times 5^{2} \]300 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 868 |
| Euler totient φ(n) | 80 |
| Square | 90000 |
| Cube | 27000000 |
| Square root | 17.320508 (= 10√3) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 16 |
| Scientific notation | 3 × |
300 in other forms
| Form | Value |
|---|---|
| In words | three hundred |
| Roman numerals | CCC |
| Binary (base 2) | 100101100 |
| Octal (base 8) | 454 |
| Hexadecimal (base 16) | 12C |
| Base 3 | 102010 |
| As time | 300 seconds = 5 min 0 s |
Is 300 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (300 ÷ 2 = 150) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (300 ÷ 3 = 100) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (300 ÷ 4 = 75) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (300 ÷ 5 = 60) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (300 ÷ 6 = 50) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (300 ÷ 10 = 30) | 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 (300 ÷ 12 = 25) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 300 a prime number?
No. 300 = × 3 × , so it is divisible by 2.
What are the factors of 300?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
What is 300 in binary?
100101100 (hexadecimal 12C, octal 454).
What is the square root of 300?
About 17.3205, exactly 10√3.
What is 300 in Roman numerals?
CCC.
Is 300 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 300?
300 is a triangular number: 1 + 2 + … + 24 = 300; a Harshad number: divisible by its digit sum 3.