The number 51984
51984 is a perfect square (228²). Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 36, 38, 48, 57 … 51984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 51984: a perfect square (228²).
- 2
51984 is composite. Its prime factorisation is
- 3
The divisors add up to 153543; without 51984 itself that is 101559, so 51984 is abundant (101559 is more than 51984). Euler's totient φ(51984) = 16416 numbers up to 51984 share no factor with it.
- 4
The digits of 51984 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 140 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51984 = 2^{4} \times 3^{2} \times 19^{2} \]51984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 153543 |
| Euler totient φ(n) | 16416 |
| Square | 2702336256 |
| Cube | 140478247931904 |
| Square root | 228 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 140 |
| Scientific notation | 5.1984 × |
| Perfect power |
51984 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand nine hundred and eighty-four |
| Binary (base 2) | 1100101100010000 |
| Octal (base 8) | 145420 |
| Hexadecimal (base 16) | CB10 |
| Base 3 | 2122022100 |
| As time | 51984 seconds = 14 h 26 min 24 s |
Is 51984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51984 ÷ 2 = 25992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51984 ÷ 3 = 17328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51984 ÷ 4 = 12996) | 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 (51984 ÷ 6 = 8664) | 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 | Yes (51984 ÷ 8 = 6498) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (51984 ÷ 9 = 5776) | 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 (51984 ÷ 12 = 4332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51984 a prime number?
No. 51984 = × × , so it is divisible by 2.
What are the factors of 51984?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 36, 38, 48, 57, 72, 76, 114, 144, 152, 171, 228, 304, 342, 361, 456, 684, 722, 912, 1083, 1368, 1444, 2166, 2736, 2888, 3249, 4332, 5776, 6498, 8664, 12996, 17328, 25992, 51984.
What is 51984 in binary?
1100101100010000 (hexadecimal CB10, octal 145420).
What is the square root of 51984?
228, because 228 × 228 = 51984.
Is 51984 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 51984?
51984 is a perfect square (228²).