The number 48144
48144 is a composite number with 40 divisors. Its prime factorisation is × 3 × 17 × 59. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 59, 68, 102 … 48144.
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How to work it out
- 1
48144 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48144 is composite. Its prime factorisation is
- 3
The divisors add up to 133920; without 48144 itself that is 85776, so 48144 is abundant (85776 is more than 48144). Euler's totient φ(48144) = 14848 numbers up to 48144 share no factor with it.
- 4
The digits of 48144 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48144 = 2^{4} \times 3 \times 17 \times 59 \]48144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 133920 |
| Euler totient φ(n) | 14848 |
| Square | 2317844736 |
| Cube | 111590316969984 |
| Square root | 219.417410 (= 4√3009) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.8144 × |
48144 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand one hundred and forty-four |
| Binary (base 2) | 1011110000010000 |
| Octal (base 8) | 136020 |
| Hexadecimal (base 16) | BC10 |
| Base 3 | 2110001010 |
| As time | 48144 seconds = 13 h 22 min 24 s |
Is 48144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48144 ÷ 2 = 24072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48144 ÷ 3 = 16048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48144 ÷ 4 = 12036) | 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 (48144 ÷ 6 = 8024) | 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 (48144 ÷ 8 = 6018) | 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 4) | 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 (48144 ÷ 12 = 4012) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48144 a prime number?
No. 48144 = × 3 × 17 × 59, so it is divisible by 2.
What are the factors of 48144?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 59, 68, 102, 118, 136, 177, 204, 236, 272, 354, 408, 472, 708, 816, 944, 1003, 1416, 2006, 2832, 3009, 4012, 6018, 8024, 12036, 16048, 24072, 48144.
What is 48144 in binary?
1011110000010000 (hexadecimal BC10, octal 136020).
What is the square root of 48144?
About 219.4174, exactly 4√3009.
Is 48144 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 48144?
It is a composite number with 40 divisors.