The number 49536
49536 is a composite number with 48 divisors. Its prime factorisation is × × 43. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 64 … 49536.
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How to work it out
- 1
What is special about 49536: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
49536 is composite. Its prime factorisation is
- 3
The divisors add up to 145860; without 49536 itself that is 96324, so 49536 is abundant (96324 is more than 49536). Euler's totient φ(49536) = 16128 numbers up to 49536 share no factor with it.
- 4
The digits of 49536 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 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49536 = 2^{7} \times 3^{2} \times 43 \]49536 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 145860 |
| Euler totient φ(n) | 16128 |
| Square | 2453815296 |
| Cube | 121552194502656 |
| Square root | 222.566844 (= 24√86) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 127 |
| Scientific notation | 4.9536 × |
49536 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand five hundred and thirty-six |
| Binary (base 2) | 1100000110000000 |
| Octal (base 8) | 140600 |
| Hexadecimal (base 16) | C180 |
| Base 3 | 2111221200 |
| As time | 49536 seconds = 13 h 45 min 36 s |
Is 49536 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49536 ÷ 2 = 24768) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49536 ÷ 3 = 16512) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49536 ÷ 4 = 12384) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (49536 ÷ 6 = 8256) | 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 (49536 ÷ 8 = 6192) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (49536 ÷ 9 = 5504) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49536 ÷ 12 = 4128) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49536 a prime number?
No. 49536 = × × 43, so it is divisible by 2.
What are the factors of 49536?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 64, 72, 86, 96, 128, 129, 144, 172, 192, 258, 288, 344, 384, 387, 516, 576, 688, 774, 1032, 1152, 1376, 1548, 2064, 2752, 3096, 4128, 5504, 6192, 8256, 12384, 16512, 24768, 49536.
What is 49536 in binary?
1100000110000000 (hexadecimal C180, octal 140600).
What is the square root of 49536?
About 222.5668, exactly 24√86.
Is 49536 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 49536?
49536 is a happy number: repeatedly adding the squares of its digits reaches 1.