The number 1023
1023 is a binary palindrome (1111111111). Its prime factorisation is 3 × 11 × 31. Divisors (8): 1, 3, 11, 31, 33, 93, 341, 1023.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1023: a binary palindrome (1111111111).
- 2
1023 is composite. Its prime factorisation is
- 3
The divisors add up to 1536; without 1023 itself that is 513, so 1023 is deficient (513 is less than 1023). Euler's totient φ(1023) = 600 numbers up to 1023 share no factor with it.
- 4
The digits of 1023 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1023 = 3 \times 11 \times 31 \]
1023 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1536 |
| Euler totient φ(n) | 600 |
| Square | 1046529 |
| Cube | 1070599167 |
| Square root | 31.984371 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 62 |
| Scientific notation | 1.023 × |
1023 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-three |
| Roman numerals | MXXIII |
| Binary (base 2) | 1111111111 |
| Octal (base 8) | 1777 |
| Hexadecimal (base 16) | 3FF |
| Base 3 | 1101220 |
| As time | 1023 seconds = 17 min 3 s |
Is 1023 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1023 ÷ 3 = 341) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1023 ÷ 11 = 93) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1023 a prime number?
No. 1023 = 3 × 11 × 31, so it is divisible by 3.
What are the factors of 1023?
1, 3, 11, 31, 33, 93, 341, 1023.
What is 1023 in binary?
1111111111 (hexadecimal 3FF, octal 1777).
What is the square root of 1023?
About 31.9844.
What is 1023 in Roman numerals?
MXXIII.
Is 1023 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 1023?
1023 is a binary palindrome (1111111111).