The number 51504
51504 is a composite number with 40 divisors. Its prime factorisation is × 3 × 29 × 37. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 37, 48, 58, 74, 87, 111 … 51504.
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How to work it out
- 1
51504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
51504 is composite. Its prime factorisation is
- 3
The divisors add up to 141360; without 51504 itself that is 89856, so 51504 is abundant (89856 is more than 51504). Euler's totient φ(51504) = 16128 numbers up to 51504 share no factor with it.
- 4
The digits of 51504 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51504 = 2^{4} \times 3 \times 29 \times 37 \]51504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 141360 |
| Euler totient φ(n) | 16128 |
| Square | 2652662016 |
| Cube | 136622704472064 |
| Square root | 226.944927 (= 4√3219) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 78 |
| Scientific notation | 5.1504 × |
51504 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand five hundred and four |
| Binary (base 2) | 1100100100110000 |
| Octal (base 8) | 144460 |
| Hexadecimal (base 16) | C930 |
| Base 3 | 2121122120 |
| As time | 51504 seconds = 14 h 18 min 24 s |
Is 51504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51504 ÷ 2 = 25752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51504 ÷ 3 = 17168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51504 ÷ 4 = 12876) | 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 (51504 ÷ 6 = 8584) | 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 | Yes (51504 ÷ 8 = 6438) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (51504 ÷ 12 = 4292) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51504 a prime number?
No. 51504 = × 3 × 29 × 37, so it is divisible by 2.
What are the factors of 51504?
1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 37, 48, 58, 74, 87, 111, 116, 148, 174, 222, 232, 296, 348, 444, 464, 592, 696, 888, 1073, 1392, 1776, 2146, 3219, 4292, 6438, 8584, 12876, 17168, 25752, 51504.
What is 51504 in binary?
1100100100110000 (hexadecimal C930, octal 144460).
What is the square root of 51504?
About 226.9449, exactly 4√3219.
Is 51504 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 51504?
It is a composite number with 40 divisors.