The number 10003
10003 is a composite number with 4 divisors. Its prime factorisation is 7 × 1429. Divisors (4): 1, 7, 1429, 10003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10003: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 1429, the product of two primes.
- 2
10003 is composite. Its prime factorisation is
- 3
The divisors add up to 11440; without 10003 itself that is 1437, so 10003 is deficient (1437 is less than 10003). Euler's totient φ(10003) = 8568 numbers up to 10003 share no factor with it.
- 4
The digits of 10003 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10003 = 7 \times 1429 \]
10003 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 11440 |
| Euler totient φ(n) | 8568 |
| Square | 100060009 |
| Cube | 1000900270027 |
| Square root | 100.014999 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 65 |
| Scientific notation | 1.0003 × |
10003 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and three |
| Binary (base 2) | 10011100010011 |
| Octal (base 8) | 23423 |
| Hexadecimal (base 16) | 2713 |
| Base 3 | 111201111 |
| As time | 10003 seconds = 2 h 46 min 43 s |
Is 10003 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 1) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10003 ÷ 7 = 1429) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10003 a prime number?
No. 10003 = 7 × 1429, so it is divisible by 7.
What are the factors of 10003?
1, 7, 1429, 10003.
What is 10003 in binary?
10011100010011 (hexadecimal 2713, octal 23423).
What is the square root of 10003?
About 100.0150.
Is 10003 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 10003?
10003 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 1429, the product of two primes.