The number 500
500 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 500: a Harshad number: divisible by its digit sum 5.
- 2
500 is composite. Its prime factorisation is
- 3
The divisors add up to 1092; without 500 itself that is 592, so 500 is abundant (592 is more than 500). Euler's totient φ(500) = 200 numbers up to 500 share no factor with it.
- 4
The digits of 500 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 110 steps to reach 1.
LaTeX source of the formulas on this page
\[ 500 = 2^{2} \times 5^{3} \]500 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1092 |
| Euler totient φ(n) | 200 |
| Square | 250000 |
| Cube | 125000000 |
| Square root | 22.360680 (= 10√5) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 110 |
| Scientific notation | 5 × |
500 in other forms
| Form | Value |
|---|---|
| In words | five hundred |
| Roman numerals | D |
| Binary (base 2) | 111110100 |
| Octal (base 8) | 764 |
| Hexadecimal (base 16) | 1F4 |
| Base 3 | 200112 |
| As time | 500 seconds = 8 min 20 s |
Is 500 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (500 ÷ 2 = 250) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (500 ÷ 4 = 125) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (500 ÷ 5 = 100) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (500 ÷ 10 = 50) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 500 a prime number?
No. 500 = × , so it is divisible by 2.
What are the factors of 500?
1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.
What is 500 in binary?
111110100 (hexadecimal 1F4, octal 764).
What is the square root of 500?
About 22.3607, exactly 10√5.
What is 500 in Roman numerals?
D.
Is 500 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 500?
500 is a Harshad number: divisible by its digit sum 5.