The number 10052
10052 is a composite number with 12 divisors. Its prime factorisation is × 7 × 359. Divisors (12): 1, 2, 4, 7, 14, 28, 359, 718, 1436, 2513, 5026, 10052.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10052 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10052 is composite. Its prime factorisation is
- 3
The divisors add up to 20160; without 10052 itself that is 10108, so 10052 is abundant (10108 is more than 10052). Euler's totient φ(10052) = 4296 numbers up to 10052 share no factor with it.
- 4
The digits of 10052 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10052 = 2^{2} \times 7 \times 359 \]10052 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 20160 |
| Euler totient φ(n) | 4296 |
| Square | 101042704 |
| Cube | 1015681260608 |
| Square root | 100.259663 (= 2√2513) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.0052 × |
10052 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and fifty-two |
| Binary (base 2) | 10011101000100 |
| Octal (base 8) | 23504 |
| Hexadecimal (base 16) | 2744 |
| Base 3 | 111210022 |
| As time | 10052 seconds = 2 h 47 min 32 s |
Is 10052 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10052 ÷ 2 = 5026) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10052 ÷ 4 = 2513) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10052 ÷ 7 = 1436) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10052 a prime number?
No. 10052 = × 7 × 359, so it is divisible by 2.
What are the factors of 10052?
1, 2, 4, 7, 14, 28, 359, 718, 1436, 2513, 5026, 10052.
What is 10052 in binary?
10011101000100 (hexadecimal 2744, octal 23504).
What is the square root of 10052?
About 100.2597, exactly 2√2513.
Is 10052 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 10052?
It is a composite number with 12 divisors.