The number 10002
10002 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 1667. Divisors (8): 1, 2, 3, 6, 1667, 3334, 5001, 10002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10002: a Harshad number: divisible by its digit sum 3.
- 2
10002 is composite. Its prime factorisation is
- 3
The divisors add up to 20016; without 10002 itself that is 10014, so 10002 is abundant (10014 is more than 10002). Euler's totient φ(10002) = 3332 numbers up to 10002 share no factor with it.
- 4
The digits of 10002 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10002 = 2 \times 3 \times 1667 \]
10002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 20016 |
| Euler totient φ(n) | 3332 |
| Square | 100040004 |
| Cube | 1000600120008 |
| Square root | 100.010000 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 65 |
| Scientific notation | 1.0002 × |
10002 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and two |
| Binary (base 2) | 10011100010010 |
| Octal (base 8) | 23422 |
| Hexadecimal (base 16) | 2712 |
| Base 3 | 111201110 |
| As time | 10002 seconds = 2 h 46 min 42 s |
Is 10002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10002 ÷ 2 = 5001) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10002 ÷ 3 = 3334) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 | Yes (10002 ÷ 6 = 1667) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10002 a prime number?
No. 10002 = 2 × 3 × 1667, so it is divisible by 2.
What are the factors of 10002?
1, 2, 3, 6, 1667, 3334, 5001, 10002.
What is 10002 in binary?
10011100010010 (hexadecimal 2712, octal 23422).
What is the square root of 10002?
About 100.0100.
Is 10002 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 10002?
10002 is a Harshad number: divisible by its digit sum 3.