The number 49984
49984 is a composite number with 28 divisors. Its prime factorisation is × 11 × 71. Divisors (28): 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 71, 88, 142, 176, 284, 352 … 49984.
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How to work it out
- 1
49984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
49984 is composite. Its prime factorisation is
- 3
The divisors add up to 109728; without 49984 itself that is 59744, so 49984 is abundant (59744 is more than 49984). Euler's totient φ(49984) = 22400 numbers up to 49984 share no factor with it.
- 4
The digits of 49984 add up to 34, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49984 = 2^{6} \times 11 \times 71 \]49984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 109728 |
| Euler totient φ(n) | 22400 |
| Square | 2498400256 |
| Cube | 124880038395904 |
| Square root | 223.571018 (= 8√781) |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 127 |
| Scientific notation | 4.9984 × |
49984 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand nine hundred and eighty-four |
| Binary (base 2) | 1100001101000000 |
| Octal (base 8) | 141500 |
| Hexadecimal (base 16) | C340 |
| Base 3 | 2112120021 |
| As time | 49984 seconds = 13 h 53 min 4 s |
Is 49984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49984 ÷ 2 = 24992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49984 ÷ 4 = 12496) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (49984 ÷ 8 = 6248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | Yes (49984 ÷ 11 = 4544) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49984 a prime number?
No. 49984 = × 11 × 71, so it is divisible by 2.
What are the factors of 49984?
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 71, 88, 142, 176, 284, 352, 568, 704, 781, 1136, 1562, 2272, 3124, 4544, 6248, 12496, 24992, 49984.
What is 49984 in binary?
1100001101000000 (hexadecimal C340, octal 141500).
What is the square root of 49984?
About 223.5710, exactly 8√781.
Is 49984 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 49984?
It is a composite number with 28 divisors.