The number 2002
2002 is a palindrome: it reads 2002 backwards too. Its prime factorisation is 2 × 7 × 11 × 13. Divisors (16): 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2002: a palindrome: it reads 2002 backwards too.
- 2
2002 is composite. Its prime factorisation is
- 3
The divisors add up to 4032; without 2002 itself that is 2030, so 2002 is abundant (2030 is more than 2002). Euler's totient φ(2002) = 720 numbers up to 2002 share no factor with it.
- 4
The digits of 2002 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2002 = 2 \times 7 \times 11 \times 13 \]
2002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4032 |
| Euler totient φ(n) | 720 |
| Square | 4008004 |
| Cube | 8024024008 |
| Square root | 44.743715 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 143 |
| Scientific notation | 2.002 × |
2002 in other forms
| Form | Value |
|---|---|
| In words | two thousand and two |
| Roman numerals | MMII |
| Binary (base 2) | 11111010010 |
| Octal (base 8) | 3722 |
| Hexadecimal (base 16) | 7D2 |
| Base 3 | 2202011 |
| As time | 2002 seconds = 33 min 22 s |
Is 2002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2002 ÷ 2 = 1001) | 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 | No (remainder 2) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2002 ÷ 7 = 286) | 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 2) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (2002 ÷ 11 = 182) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2002 a prime number?
No. 2002 = 2 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 2002?
1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
What is 2002 in binary?
11111010010 (hexadecimal 7D2, octal 3722).
What is the square root of 2002?
About 44.7437.
What is 2002 in Roman numerals?
MMII.
Is 2002 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 2002?
2002 is a palindrome: it reads 2002 backwards too.