The number 7008
7008 is a composite number with 24 divisors. Its prime factorisation is × 3 × 73. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292 … 7008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
7008 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
7008 is composite. Its prime factorisation is
- 3
The divisors add up to 18648; without 7008 itself that is 11640, so 7008 is abundant (11640 is more than 7008). Euler's totient φ(7008) = 2304 numbers up to 7008 share no factor with it.
- 4
The digits of 7008 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 57 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7008 = 2^{5} \times 3 \times 73 \]7008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 18648 |
| Euler totient φ(n) | 2304 |
| Square | 49112064 |
| Cube | 344177344512 |
| Square root | 83.713798 (= 4√438) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 57 |
| Scientific notation | 7.008 × |
7008 in other forms
| Form | Value |
|---|---|
| In words | seven thousand and eight |
| Binary (base 2) | 1101101100000 |
| Octal (base 8) | 15540 |
| Hexadecimal (base 16) | 1B60 |
| Base 3 | 100121120 |
| As time | 7008 seconds = 1 h 56 min 48 s |
Is 7008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7008 ÷ 2 = 3504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7008 ÷ 3 = 2336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7008 ÷ 4 = 1752) | 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 | Yes (7008 ÷ 6 = 1168) | 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 | Yes (7008 ÷ 8 = 876) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7008 ÷ 12 = 584) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7008 a prime number?
No. 7008 = × 3 × 73, so it is divisible by 2.
What are the factors of 7008?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008.
What is 7008 in binary?
1101101100000 (hexadecimal 1B60, octal 15540).
What is the square root of 7008?
About 83.7138, exactly 4√438.
Is 7008 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 7008?
It is a composite number with 24 divisors.