The number 48000
48000 is a composite number with 64 divisors. Its prime factorisation is × 3 × . Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 48000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48000: a Harshad number: divisible by its digit sum 12.
- 2
48000 is composite. Its prime factorisation is
- 3
The divisors add up to 159120; without 48000 itself that is 111120, so 48000 is abundant (111120 is more than 48000). Euler's totient φ(48000) = 12800 numbers up to 48000 share no factor with it.
- 4
The digits of 48000 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48000 = 2^{7} \times 3 \times 5^{3} \]48000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 159120 |
| Euler totient φ(n) | 12800 |
| Square | 2304000000 |
| Cube | 110592000000000 |
| Square root | 219.089023 (= 40√30) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.8 × |
48000 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand |
| Binary (base 2) | 1011101110000000 |
| Octal (base 8) | 135600 |
| Hexadecimal (base 16) | BB80 |
| Base 3 | 2102211210 |
| As time | 48000 seconds = 13 h 20 min 0 s |
Is 48000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48000 ÷ 2 = 24000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48000 ÷ 3 = 16000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48000 ÷ 4 = 12000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48000 ÷ 5 = 9600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48000 ÷ 6 = 8000) | 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 (48000 ÷ 8 = 6000) | 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 | Yes (48000 ÷ 10 = 4800) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48000 ÷ 12 = 4000) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48000 a prime number?
No. 48000 = × 3 × , so it is divisible by 2.
What are the factors of 48000?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 125, 128, 150, 160, 192, 200, 240, 250, 300, 320, 375, 384, 400, 480, 500, 600, 640, 750, 800, 960, 1000, 1200, 1500, 1600, 1920, 2000, 2400, 3000, 3200, 4000, 4800, 6000, 8000, 9600, 12000, 16000, 24000, 48000.
What is 48000 in binary?
1011101110000000 (hexadecimal BB80, octal 135600).
What is the square root of 48000?
About 219.0890, exactly 40√30.
Is 48000 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 48000?
48000 is a Harshad number: divisible by its digit sum 12.