The number 4048
4048 is a composite number with 20 divisors. Its prime factorisation is × 11 × 23. Divisors (20): 1, 2, 4, 8, 11, 16, 22, 23, 44, 46, 88, 92, 176, 184, 253, 368 … 4048.
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How to work it out
- 1
What is special about 4048: a Harshad number: divisible by its digit sum 16.
- 2
4048 is composite. Its prime factorisation is
- 3
The divisors add up to 8928; without 4048 itself that is 4880, so 4048 is abundant (4880 is more than 4048). Euler's totient φ(4048) = 1760 numbers up to 4048 share no factor with it.
- 4
The digits of 4048 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4048 = 2^{4} \times 11 \times 23 \]4048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 8928 |
| Euler totient φ(n) | 1760 |
| Square | 16386304 |
| Cube | 66331758592 |
| Square root | 63.623895 (= 4√253) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 113 |
| Scientific notation | 4.048 × |
4048 in other forms
| Form | Value |
|---|---|
| In words | four thousand and forty-eight |
| Binary (base 2) | 111111010000 |
| Octal (base 8) | 7720 |
| Hexadecimal (base 16) | FD0 |
| Base 3 | 12112221 |
| As time | 4048 seconds = 1 h 7 min 28 s |
Is 4048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4048 ÷ 2 = 2024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4048 ÷ 4 = 1012) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (4048 ÷ 8 = 506) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | Yes (4048 ÷ 11 = 368) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4048 a prime number?
No. 4048 = × 11 × 23, so it is divisible by 2.
What are the factors of 4048?
1, 2, 4, 8, 11, 16, 22, 23, 44, 46, 88, 92, 176, 184, 253, 368, 506, 1012, 2024, 4048.
What is 4048 in binary?
111111010000 (hexadecimal FD0, octal 7720).
What is the square root of 4048?
About 63.6239, exactly 4√253.
Is 4048 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 4048?
4048 is a Harshad number: divisible by its digit sum 16.