The number 504
504 is a composite number with 24 divisors. Its prime factorisation is × × 7. Divisors (24): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42 … 504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 504: a Harshad number: divisible by its digit sum 9.
- 2
504 is composite. Its prime factorisation is
- 3
The divisors add up to 1560; without 504 itself that is 1056, so 504 is abundant (1056 is more than 504). Euler's totient φ(504) = 144 numbers up to 504 share no factor with it.
- 4
The digits of 504 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 110 steps to reach 1.
LaTeX source of the formulas on this page
\[ 504 = 2^{3} \times 3^{2} \times 7 \]504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1560 |
| Euler totient φ(n) | 144 |
| Square | 254016 |
| Cube | 128024064 |
| Square root | 22.449944 (= 6√14) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 110 |
| Scientific notation | 5.04 × |
504 in other forms
| Form | Value |
|---|---|
| In words | five hundred and four |
| Roman numerals | DIV |
| Binary (base 2) | 111111000 |
| Octal (base 8) | 770 |
| Hexadecimal (base 16) | 1F8 |
| Base 3 | 200200 |
| As time | 504 seconds = 8 min 24 s |
Is 504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (504 ÷ 2 = 252) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (504 ÷ 3 = 168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (504 ÷ 4 = 126) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (504 ÷ 6 = 84) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (504 ÷ 7 = 72) | 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 | Yes (504 ÷ 8 = 63) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (504 ÷ 9 = 56) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (504 ÷ 12 = 42) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 504 a prime number?
No. 504 = × × 7, so it is divisible by 2.
What are the factors of 504?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.
What is 504 in binary?
111111000 (hexadecimal 1F8, octal 770).
What is the square root of 504?
About 22.4499, exactly 6√14.
What is 504 in Roman numerals?
DIV.
Is 504 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 504?
504 is a Harshad number: divisible by its digit sum 9.