The number 20008
20008 is a composite number with 16 divisors. Its prime factorisation is × 41 × 61. Divisors (16): 1, 2, 4, 8, 41, 61, 82, 122, 164, 244, 328, 488, 2501, 5002, 10004, 20008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20008: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
20008 is composite. Its prime factorisation is
- 3
The divisors add up to 39060; without 20008 itself that is 19052, so 20008 is deficient (19052 is less than 20008). Euler's totient φ(20008) = 9600 numbers up to 20008 share no factor with it.
- 4
The digits of 20008 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 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20008 = 2^{3} \times 41 \times 61 \]20008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 39060 |
| Euler totient φ(n) | 9600 |
| Square | 400320064 |
| Cube | 8009603840512 |
| Square root | 141.449638 (= 2√5002) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.0008 × |
20008 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand and eight |
| Binary (base 2) | 100111000101000 |
| Octal (base 8) | 47050 |
| Hexadecimal (base 16) | 4E28 |
| Base 3 | 1000110001 |
| As time | 20008 seconds = 5 h 33 min 28 s |
Is 20008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20008 ÷ 2 = 10004) | 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 (20008 ÷ 4 = 5002) | 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 | No (remainder 2) | 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 (20008 ÷ 8 = 2501) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 20008 a prime number?
No. 20008 = × 41 × 61, so it is divisible by 2.
What are the factors of 20008?
1, 2, 4, 8, 41, 61, 82, 122, 164, 244, 328, 488, 2501, 5002, 10004, 20008.
What is 20008 in binary?
100111000101000 (hexadecimal 4E28, octal 47050).
What is the square root of 20008?
About 141.4496, exactly 2√5002.
Is 20008 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 20008?
20008 is a happy number: repeatedly adding the squares of its digits reaches 1.