The number 42048
42048 is a composite number with 42 divisors. Its prime factorisation is × × 73. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 42048.
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How to work it out
- 1
What is special about 42048: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
42048 is composite. Its prime factorisation is
- 3
The divisors add up to 122174; without 42048 itself that is 80126, so 42048 is abundant (80126 is more than 42048). Euler's totient φ(42048) = 13824 numbers up to 42048 share no factor with it.
- 4
The digits of 42048 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 57 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42048 = 2^{6} \times 3^{2} \times 73 \]42048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 122174 |
| Euler totient φ(n) | 13824 |
| Square | 1768034304 |
| Cube | 74342306414592 |
| Square root | 205.056090 (= 24√73) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 57 |
| Scientific notation | 4.2048 × |
42048 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand and forty-eight |
| Binary (base 2) | 1010010001000000 |
| Octal (base 8) | 122100 |
| Hexadecimal (base 16) | A440 |
| Base 3 | 2010200100 |
| As time | 42048 seconds = 11 h 40 min 48 s |
Is 42048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42048 ÷ 2 = 21024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42048 ÷ 3 = 14016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42048 ÷ 4 = 10512) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (42048 ÷ 6 = 7008) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (42048 ÷ 8 = 5256) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (42048 ÷ 9 = 4672) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42048 ÷ 12 = 3504) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42048 a prime number?
No. 42048 = × × 73, so it is divisible by 2.
What are the factors of 42048?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 73, 96, 144, 146, 192, 219, 288, 292, 438, 576, 584, 657, 876, 1168, 1314, 1752, 2336, 2628, 3504, 4672, 5256, 7008, 10512, 14016, 21024, 42048.
What is 42048 in binary?
1010010001000000 (hexadecimal A440, octal 122100).
What is the square root of 42048?
About 205.0561, exactly 24√73.
Is 42048 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 42048?
42048 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.