The number 1052
1052 is a composite number with 6 divisors. Its prime factorisation is × 263. Divisors (6): 1, 2, 4, 263, 526, 1052.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1052 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1052 is composite. Its prime factorisation is
- 3
The divisors add up to 1848; without 1052 itself that is 796, so 1052 is deficient (796 is less than 1052). Euler's totient φ(1052) = 524 numbers up to 1052 share no factor with it.
- 4
The digits of 1052 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 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1052 = 2^{2} \times 263 \]1052 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 1848 |
| Euler totient φ(n) | 524 |
| Square | 1106704 |
| Cube | 1164252608 |
| Square root | 32.434549 (= 2√263) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 80 |
| Scientific notation | 1.052 × |
1052 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-two |
| Roman numerals | MLII |
| Binary (base 2) | 10000011100 |
| Octal (base 8) | 2034 |
| Hexadecimal (base 16) | 41C |
| Base 3 | 1102222 |
| As time | 1052 seconds = 17 min 32 s |
Is 1052 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1052 ÷ 2 = 526) | 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 (1052 ÷ 4 = 263) | 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 | 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 | 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 7) | 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 1052 a prime number?
No. 1052 = × 263, so it is divisible by 2.
What are the factors of 1052?
1, 2, 4, 263, 526, 1052.
What is 1052 in binary?
10000011100 (hexadecimal 41C, octal 2034).
What is the square root of 1052?
About 32.4345, exactly 2√263.
What is 1052 in Roman numerals?
MLII.
Is 1052 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 1052?
It is a composite number with 6 divisors.