The number 516
516 is a composite number with 12 divisors. Its prime factorisation is × 3 × 43. Divisors (12): 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 516: a Harshad number: divisible by its digit sum 12.
- 2
516 is composite. Its prime factorisation is
- 3
The divisors add up to 1232; without 516 itself that is 716, so 516 is abundant (716 is more than 516). Euler's totient φ(516) = 168 numbers up to 516 share no factor with it.
- 4
The digits of 516 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 123 steps to reach 1.
LaTeX source of the formulas on this page
\[ 516 = 2^{2} \times 3 \times 43 \]516 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1232 |
| Euler totient φ(n) | 168 |
| Square | 266256 |
| Cube | 137388096 |
| Square root | 22.715633 (= 2√129) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 123 |
| Scientific notation | 5.16 × |
516 in other forms
| Form | Value |
|---|---|
| In words | five hundred and sixteen |
| Roman numerals | DXVI |
| Binary (base 2) | 1000000100 |
| Octal (base 8) | 1004 |
| Hexadecimal (base 16) | 204 |
| Base 3 | 201010 |
| As time | 516 seconds = 8 min 36 s |
Is 516 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (516 ÷ 2 = 258) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (516 ÷ 3 = 172) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (516 ÷ 4 = 129) | 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 | Yes (516 ÷ 6 = 86) | 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 | 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 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (516 ÷ 12 = 43) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 516 a prime number?
No. 516 = × 3 × 43, so it is divisible by 2.
What are the factors of 516?
1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516.
What is 516 in binary?
1000000100 (hexadecimal 204, octal 1004).
What is the square root of 516?
About 22.7156, exactly 2√129.
What is 516 in Roman numerals?
DXVI.
Is 516 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 516?
516 is a Harshad number: divisible by its digit sum 12.