The number 49152
49152 is a composite number with 30 divisors. Its prime factorisation is × 3. Divisors (30): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256 … 49152.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
49152 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
49152 is composite. Its prime factorisation is
- 3
The divisors add up to 131068; without 49152 itself that is 81916, so 49152 is abundant (81916 is more than 49152). Euler's totient φ(49152) = 16384 numbers up to 49152 share no factor with it.
- 4
The digits of 49152 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49152 = 2^{14} \times 3 \]49152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 131068 |
| Euler totient φ(n) | 16384 |
| Square | 2415919104 |
| Cube | 118747255799808 |
| Square root | 221.702503 (= 128√3) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 21 |
| Scientific notation | 4.9152 × |
49152 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand one hundred and fifty-two |
| Binary (base 2) | 1100000000000000 |
| Octal (base 8) | 140000 |
| Hexadecimal (base 16) | C000 |
| Base 3 | 2111102110 |
| As time | 49152 seconds = 13 h 39 min 12 s |
Is 49152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49152 ÷ 2 = 24576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49152 ÷ 3 = 16384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49152 ÷ 4 = 12288) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (49152 ÷ 6 = 8192) | 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 (49152 ÷ 8 = 6144) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49152 ÷ 12 = 4096) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49152 a prime number?
No. 49152 = × 3, so it is divisible by 2.
What are the factors of 49152?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 49152.
What is 49152 in binary?
1100000000000000 (hexadecimal C000, octal 140000).
What is the square root of 49152?
About 221.7025, exactly 128√3.
Is 49152 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 49152?
It is a composite number with 30 divisors.