The number 8008
8008 is a palindrome: it reads 8008 backwards too. Its prime factorisation is × 7 × 11 × 13. Divisors (32): 1, 2, 4, 7, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88 … 8008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8008: a palindrome: it reads 8008 backwards too.
- 2
8008 is composite. Its prime factorisation is
- 3
The divisors add up to 20160; without 8008 itself that is 12152, so 8008 is abundant (12152 is more than 8008). Euler's totient φ(8008) = 2880 numbers up to 8008 share no factor with it.
- 4
The digits of 8008 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8008 = 2^{3} \times 7 \times 11 \times 13 \]8008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 20160 |
| Euler totient φ(n) | 2880 |
| Square | 64128064 |
| Cube | 513537536512 |
| Square root | 89.487429 (= 2√2002) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 145 |
| Scientific notation | 8.008 × |
8008 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and eight |
| Binary (base 2) | 1111101001000 |
| Octal (base 8) | 17510 |
| Hexadecimal (base 16) | 1F48 |
| Base 3 | 101222121 |
| As time | 8008 seconds = 2 h 13 min 28 s |
Is 8008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8008 ÷ 2 = 4004) | 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 | Yes (8008 ÷ 4 = 2002) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (8008 ÷ 7 = 1144) | 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 | Yes (8008 ÷ 8 = 1001) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (8008 ÷ 11 = 728) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8008 a prime number?
No. 8008 = × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 8008?
1, 2, 4, 7, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 104, 143, 154, 182, 286, 308, 364, 572, 616, 728, 1001, 1144, 2002, 4004, 8008.
What is 8008 in binary?
1111101001000 (hexadecimal 1F48, octal 17510).
What is the square root of 8008?
About 89.4874, exactly 2√2002.
Is 8008 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 8008?
8008 is a palindrome: it reads 8008 backwards too.