The number 506
506 is a composite number with 8 divisors. Its prime factorisation is 2 × 11 × 23. Divisors (8): 1, 2, 11, 22, 23, 46, 253, 506.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 506: a Harshad number: divisible by its digit sum 11.
- 2
506 is composite. Its prime factorisation is
- 3
The divisors add up to 864; without 506 itself that is 358, so 506 is deficient (358 is less than 506). Euler's totient φ(506) = 220 numbers up to 506 share no factor with it.
- 4
The digits of 506 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 110 steps to reach 1.
LaTeX source of the formulas on this page
\[ 506 = 2 \times 11 \times 23 \]
506 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 864 |
| Euler totient φ(n) | 220 |
| Square | 256036 |
| Cube | 129554216 |
| Square root | 22.494444 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 110 |
| Scientific notation | 5.06 × |
506 in other forms
| Form | Value |
|---|---|
| In words | five hundred and six |
| Roman numerals | DVI |
| Binary (base 2) | 111111010 |
| Octal (base 8) | 772 |
| Hexadecimal (base 16) | 1FA |
| Base 3 | 200202 |
| As time | 506 seconds = 8 min 26 s |
Is 506 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (506 ÷ 2 = 253) | 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 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 2) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (506 ÷ 11 = 46) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 506 a prime number?
No. 506 = 2 × 11 × 23, so it is divisible by 2.
What are the factors of 506?
1, 2, 11, 22, 23, 46, 253, 506.
What is 506 in binary?
111111010 (hexadecimal 1FA, octal 772).
What is the square root of 506?
About 22.4944.
What is 506 in Roman numerals?
DVI.
Is 506 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 506?
506 is a Harshad number: divisible by its digit sum 11.