The number 49728
49728 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 37. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42 … 49728.
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How to work it out
- 1
49728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
49728 is composite. Its prime factorisation is
- 3
The divisors add up to 154432; without 49728 itself that is 104704, so 49728 is abundant (104704 is more than 49728). Euler's totient φ(49728) = 13824 numbers up to 49728 share no factor with it.
- 4
The digits of 49728 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49728 = 2^{6} \times 3 \times 7 \times 37 \]49728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 154432 |
| Euler totient φ(n) | 13824 |
| Square | 2472873984 |
| Cube | 122971077476352 |
| Square root | 222.997758 (= 8√777) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 39 |
| Scientific notation | 4.9728 × |
49728 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand seven hundred and twenty-eight |
| Binary (base 2) | 1100001001000000 |
| Octal (base 8) | 141100 |
| Hexadecimal (base 16) | C240 |
| Base 3 | 2112012210 |
| As time | 49728 seconds = 13 h 48 min 48 s |
Is 49728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49728 ÷ 2 = 24864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49728 ÷ 3 = 16576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49728 ÷ 4 = 12432) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (49728 ÷ 6 = 8288) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (49728 ÷ 7 = 7104) | 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 (49728 ÷ 8 = 6216) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49728 ÷ 12 = 4144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49728 a prime number?
No. 49728 = × 3 × 7 × 37, so it is divisible by 2.
What are the factors of 49728?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42, 48, 56, 64, 74, 84, 96, 111, 112, 148, 168, 192, 222, 224, 259, 296, 336, 444, 448, 518, 592, 672, 777, 888, 1036, 1184, 1344, 1554, 1776, 2072, 2368, 3108, 3552, 4144, 6216, 7104, 8288, 12432, 16576, 24864, 49728.
What is 49728 in binary?
1100001001000000 (hexadecimal C240, octal 141100).
What is the square root of 49728?
About 222.9978, exactly 8√777.
Is 49728 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 49728?
It is a composite number with 56 divisors.