The number 7007
7007 is a palindrome: it reads 7007 backwards too. Its prime factorisation is × 11 × 13. Divisors (12): 1, 7, 11, 13, 49, 77, 91, 143, 539, 637, 1001, 7007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7007: a palindrome: it reads 7007 backwards too.
- 2
7007 is composite. Its prime factorisation is
- 3
The divisors add up to 9576; without 7007 itself that is 2569, so 7007 is deficient (2569 is less than 7007). Euler's totient φ(7007) = 5040 numbers up to 7007 share no factor with it.
- 4
The digits of 7007 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 88 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7007 = 7^{2} \times 11 \times 13 \]7007 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 9576 |
| Euler totient φ(n) | 5040 |
| Square | 49098049 |
| Cube | 344030029343 |
| Square root | 83.707825 (= 7√143) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 88 |
| Scientific notation | 7.007 × |
7007 in other forms
| Form | Value |
|---|---|
| In words | seven thousand and seven |
| Binary (base 2) | 1101101011111 |
| Octal (base 8) | 15537 |
| Hexadecimal (base 16) | 1B5F |
| Base 3 | 100121112 |
| As time | 7007 seconds = 1 h 56 min 47 s |
Is 7007 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 3) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7007 ÷ 7 = 1001) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (7007 ÷ 11 = 637) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7007 a prime number?
No. 7007 = × 11 × 13, so it is divisible by 7.
What are the factors of 7007?
1, 7, 11, 13, 49, 77, 91, 143, 539, 637, 1001, 7007.
What is 7007 in binary?
1101101011111 (hexadecimal 1B5F, octal 15537).
What is the square root of 7007?
About 83.7078, exactly 7√143.
Is 7007 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 7007?
7007 is a palindrome: it reads 7007 backwards too.