The number 20007
20007 is a composite number with 20 divisors. Its prime factorisation is × 13 × 19. Divisors (20): 1, 3, 9, 13, 19, 27, 39, 57, 81, 117, 171, 247, 351, 513, 741, 1053 … 20007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20007: a Harshad number: divisible by its digit sum 9.
- 2
20007 is composite. Its prime factorisation is
- 3
The divisors add up to 33880; without 20007 itself that is 13873, so 20007 is deficient (13873 is less than 20007). Euler's totient φ(20007) = 11664 numbers up to 20007 share no factor with it.
- 4
The digits of 20007 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20007 = 3^{4} \times 13 \times 19 \]20007 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 33880 |
| Euler totient φ(n) | 11664 |
| Square | 400280049 |
| Cube | 8008402940343 |
| Square root | 141.446103 (= 9√247) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 92 |
| Scientific notation | 2.0007 × |
20007 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand and seven |
| Binary (base 2) | 100111000100111 |
| Octal (base 8) | 47047 |
| Hexadecimal (base 16) | 4E27 |
| Base 3 | 1000110000 |
| As time | 20007 seconds = 5 h 33 min 27 s |
Is 20007 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 | Yes (20007 ÷ 3 = 6669) | 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 3) | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (20007 ÷ 9 = 2223) | 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 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20007 a prime number?
No. 20007 = × 13 × 19, so it is divisible by 3.
What are the factors of 20007?
1, 3, 9, 13, 19, 27, 39, 57, 81, 117, 171, 247, 351, 513, 741, 1053, 1539, 2223, 6669, 20007.
What is 20007 in binary?
100111000100111 (hexadecimal 4E27, octal 47047).
What is the square root of 20007?
About 141.4461, exactly 9√247.
Is 20007 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 20007?
20007 is a Harshad number: divisible by its digit sum 9.