The number 1001
1001 is a palindrome: it reads 1001 backwards too. Its prime factorisation is 7 × 11 × 13. Divisors (8): 1, 7, 11, 13, 77, 91, 143, 1001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1001: a palindrome: it reads 1001 backwards too.
- 2
1001 is composite. Its prime factorisation is
- 3
The divisors add up to 1344; without 1001 itself that is 343, so 1001 is deficient (343 is less than 1001). Euler's totient φ(1001) = 720 numbers up to 1001 share no factor with it.
- 4
The digits of 1001 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 142 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1001 = 7 \times 11 \times 13 \]
1001 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1344 |
| Euler totient φ(n) | 720 |
| Square | 1002001 |
| Cube | 1003003001 |
| Square root | 31.638584 |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 142 |
| Scientific notation | 1.001 × |
1001 in other forms
| Form | Value |
|---|---|
| In words | one thousand and one |
| Roman numerals | MI |
| Binary (base 2) | 1111101001 |
| Octal (base 8) | 1751 |
| Hexadecimal (base 16) | 3E9 |
| Base 3 | 1101002 |
| As time | 1001 seconds = 16 min 41 s |
Is 1001 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 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1001 ÷ 7 = 143) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1001 ÷ 11 = 91) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1001 a prime number?
No. 1001 = 7 × 11 × 13, so it is divisible by 7.
What are the factors of 1001?
1, 7, 11, 13, 77, 91, 143, 1001.
What is 1001 in binary?
1111101001 (hexadecimal 3E9, octal 1751).
What is the square root of 1001?
About 31.6386.
What is 1001 in Roman numerals?
MI.
Is 1001 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 1001?
1001 is a palindrome: it reads 1001 backwards too.