The number 48006
48006 is a composite number with 32 divisors. Its prime factorisation is 2 × × 7 × 127. Divisors (32): 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 127, 189 … 48006.
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How to work it out
- 1
What is special about 48006: a Harshad number: divisible by its digit sum 18.
- 2
48006 is composite. Its prime factorisation is
- 3
The divisors add up to 122880; without 48006 itself that is 74874, so 48006 is abundant (74874 is more than 48006). Euler's totient φ(48006) = 13608 numbers up to 48006 share no factor with it.
- 4
The digits of 48006 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48006 = 2 \times 3^{3} \times 7 \times 127 \]48006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 122880 |
| Euler totient φ(n) | 13608 |
| Square | 2304576036 |
| Cube | 110633477184216 |
| Square root | 219.102716 (= 3√5334) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.8006 × |
48006 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand and six |
| Binary (base 2) | 1011101110000110 |
| Octal (base 8) | 135606 |
| Hexadecimal (base 16) | BB86 |
| Base 3 | 2102212000 |
| As time | 48006 seconds = 13 h 20 min 6 s |
Is 48006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48006 ÷ 2 = 24003) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48006 ÷ 3 = 16002) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (48006 ÷ 6 = 8001) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (48006 ÷ 7 = 6858) | 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 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48006 ÷ 9 = 5334) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48006 a prime number?
No. 48006 = 2 × × 7 × 127, so it is divisible by 2.
What are the factors of 48006?
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 127, 189, 254, 378, 381, 762, 889, 1143, 1778, 2286, 2667, 3429, 5334, 6858, 8001, 16002, 24003, 48006.
What is 48006 in binary?
1011101110000110 (hexadecimal BB86, octal 135606).
What is the square root of 48006?
About 219.1027, exactly 3√5334.
Is 48006 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 48006?
48006 is a Harshad number: divisible by its digit sum 18.