The number 5005
5005 is a palindrome: it reads 5005 backwards too. Its prime factorisation is 5 × 7 × 11 × 13. Divisors (16): 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5005: a palindrome: it reads 5005 backwards too.
- 2
5005 is composite. Its prime factorisation is
- 3
The divisors add up to 8064; without 5005 itself that is 3059, so 5005 is deficient (3059 is less than 5005). Euler's totient φ(5005) = 2880 numbers up to 5005 share no factor with it.
- 4
The digits of 5005 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5005 = 5 \times 7 \times 11 \times 13 \]
5005 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 8064 |
| Euler totient φ(n) | 2880 |
| Square | 25050025 |
| Cube | 125375375125 |
| Square root | 70.746025 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 28 |
| Scientific notation | 5.005 × |
5005 in other forms
| Form | Value |
|---|---|
| In words | five thousand and five |
| Binary (base 2) | 1001110001101 |
| Octal (base 8) | 11615 |
| Hexadecimal (base 16) | 138D |
| Base 3 | 20212101 |
| As time | 5005 seconds = 1 h 23 min 25 s |
Is 5005 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 1) | 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 | Yes (5005 ÷ 5 = 1001) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5005 ÷ 7 = 715) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (5005 ÷ 11 = 455) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5005 a prime number?
No. 5005 = 5 × 7 × 11 × 13, so it is divisible by 5.
What are the factors of 5005?
1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005.
What is 5005 in binary?
1001110001101 (hexadecimal 138D, octal 11615).
What is the square root of 5005?
About 70.7460.
Is 5005 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 5005?
5005 is a palindrome: it reads 5005 backwards too.