The number 49344
49344 is a composite number with 28 divisors. Its prime factorisation is × 3 × 257. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 257, 514 … 49344.
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How to work it out
- 1
What is special about 49344: a Harshad number: divisible by its digit sum 24.
- 2
49344 is composite. Its prime factorisation is
- 3
The divisors add up to 131064; without 49344 itself that is 81720, so 49344 is abundant (81720 is more than 49344). Euler's totient φ(49344) = 16384 numbers up to 49344 share no factor with it.
- 4
The digits of 49344 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49344 = 2^{6} \times 3 \times 257 \]49344 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 131064 |
| Euler totient φ(n) | 16384 |
| Square | 2434830336 |
| Cube | 120144268099584 |
| Square root | 222.135094 (= 8√771) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 39 |
| Scientific notation | 4.9344 × |
49344 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand three hundred and forty-four |
| Binary (base 2) | 1100000011000000 |
| Octal (base 8) | 140300 |
| Hexadecimal (base 16) | C0C0 |
| Base 3 | 2111200120 |
| As time | 49344 seconds = 13 h 42 min 24 s |
Is 49344 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49344 ÷ 2 = 24672) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49344 ÷ 3 = 16448) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49344 ÷ 4 = 12336) | 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 (49344 ÷ 6 = 8224) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (49344 ÷ 8 = 6168) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49344 ÷ 12 = 4112) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49344 a prime number?
No. 49344 = × 3 × 257, so it is divisible by 2.
What are the factors of 49344?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 257, 514, 771, 1028, 1542, 2056, 3084, 4112, 6168, 8224, 12336, 16448, 24672, 49344.
What is 49344 in binary?
1100000011000000 (hexadecimal C0C0, octal 140300).
What is the square root of 49344?
About 222.1351, exactly 8√771.
Is 49344 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 49344?
49344 is a Harshad number: divisible by its digit sum 24.