The number 10048
10048 is a composite number with 14 divisors. Its prime factorisation is × 157. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 157, 314, 628, 1256, 2512, 5024, 10048.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10048 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10048 is composite. Its prime factorisation is
- 3
The divisors add up to 20066; without 10048 itself that is 10018, so 10048 is deficient (10018 is less than 10048). Euler's totient φ(10048) = 4992 numbers up to 10048 share no factor with it.
- 4
The digits of 10048 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10048 = 2^{6} \times 157 \]10048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 20066 |
| Euler totient φ(n) | 4992 |
| Square | 100962304 |
| Cube | 1014469230592 |
| Square root | 100.239713 (= 8√157) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0048 × |
10048 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and forty-eight |
| Binary (base 2) | 10011101000000 |
| Octal (base 8) | 23500 |
| Hexadecimal (base 16) | 2740 |
| Base 3 | 111210011 |
| As time | 10048 seconds = 2 h 47 min 28 s |
Is 10048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10048 ÷ 2 = 5024) | 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 (10048 ÷ 4 = 2512) | 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 3) | 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 (10048 ÷ 8 = 1256) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 5) | 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 10048 a prime number?
No. 10048 = × 157, so it is divisible by 2.
What are the factors of 10048?
1, 2, 4, 8, 16, 32, 64, 157, 314, 628, 1256, 2512, 5024, 10048.
What is 10048 in binary?
10011101000000 (hexadecimal 2740, octal 23500).
What is the square root of 10048?
About 100.2397, exactly 8√157.
Is 10048 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 10048?
It is a composite number with 14 divisors.