The number 48576
48576 is a composite number with 56 divisors. Its prime factorisation is × 3 × 11 × 23. Divisors (56): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 32, 33, 44, 46 … 48576.
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How to work it out
- 1
What is special about 48576: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
48576 is composite. Its prime factorisation is
- 3
The divisors add up to 146304; without 48576 itself that is 97728, so 48576 is abundant (97728 is more than 48576). Euler's totient φ(48576) = 14080 numbers up to 48576 share no factor with it.
- 4
The digits of 48576 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 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48576 = 2^{6} \times 3 \times 11 \times 23 \]48576 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 146304 |
| Euler totient φ(n) | 14080 |
| Square | 2359627776 |
| Cube | 114621278846976 |
| Square root | 220.399637 (= 8√759) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 65 |
| Scientific notation | 4.8576 × |
48576 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand five hundred and seventy-six |
| Binary (base 2) | 1011110111000000 |
| Octal (base 8) | 136700 |
| Hexadecimal (base 16) | BDC0 |
| Base 3 | 2110122010 |
| As time | 48576 seconds = 13 h 29 min 36 s |
Is 48576 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48576 ÷ 2 = 24288) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48576 ÷ 3 = 16192) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48576 ÷ 4 = 12144) | 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 (48576 ÷ 6 = 8096) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (48576 ÷ 8 = 6072) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (48576 ÷ 11 = 4416) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48576 ÷ 12 = 4048) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48576 a prime number?
No. 48576 = × 3 × 11 × 23, so it is divisible by 2.
What are the factors of 48576?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 32, 33, 44, 46, 48, 64, 66, 69, 88, 92, 96, 132, 138, 176, 184, 192, 253, 264, 276, 352, 368, 506, 528, 552, 704, 736, 759, 1012, 1056, 1104, 1472, 1518, 2024, 2112, 2208, 3036, 4048, 4416, 6072, 8096, 12144, 16192, 24288, 48576.
What is 48576 in binary?
1011110111000000 (hexadecimal BDC0, octal 136700).
What is the square root of 48576?
About 220.3996, exactly 8√759.
Is 48576 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 48576?
48576 is a happy number: repeatedly adding the squares of its digits reaches 1.