The number 48672
48672 is a composite number with 54 divisors. Its prime factorisation is × × . Divisors (54): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 48672.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
48672 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48672 is composite. Its prime factorisation is
- 3
The divisors add up to 149877; without 48672 itself that is 101205, so 48672 is abundant (101205 is more than 48672). Euler's totient φ(48672) = 14976 numbers up to 48672 share no factor with it.
- 4
The digits of 48672 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 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48672 = 2^{5} \times 3^{2} \times 13^{2} \]48672 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 149877 |
| Euler totient φ(n) | 14976 |
| Square | 2368963584 |
| Cube | 115302195560448 |
| Square root | 220.617316 (= 156√2) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 114 |
| Scientific notation | 4.8672 × |
48672 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand six hundred and seventy-two |
| Binary (base 2) | 1011111000100000 |
| Octal (base 8) | 137040 |
| Hexadecimal (base 16) | BE20 |
| Base 3 | 2110202200 |
| As time | 48672 seconds = 13 h 31 min 12 s |
Is 48672 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48672 ÷ 2 = 24336) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48672 ÷ 3 = 16224) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48672 ÷ 4 = 12168) | 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 (48672 ÷ 6 = 8112) | 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 (48672 ÷ 8 = 6084) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48672 ÷ 9 = 5408) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48672 ÷ 12 = 4056) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48672 a prime number?
No. 48672 = × × , so it is divisible by 2.
What are the factors of 48672?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 169, 208, 234, 288, 312, 338, 416, 468, 507, 624, 676, 936, 1014, 1248, 1352, 1521, 1872, 2028, 2704, 3042, 3744, 4056, 5408, 6084, 8112, 12168, 16224, 24336, 48672.
What is 48672 in binary?
1011111000100000 (hexadecimal BE20, octal 137040).
What is the square root of 48672?
About 220.6173, exactly 156√2.
Is 48672 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 48672?
It is a composite number with 54 divisors.