The number 1003
1003 is a composite number with 4 divisors. Its prime factorisation is 17 × 59. Divisors (4): 1, 17, 59, 1003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1003: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 17 × 59, the product of two primes.
- 2
1003 is composite. Its prime factorisation is
- 3
The divisors add up to 1080; without 1003 itself that is 77, so 1003 is deficient (77 is less than 1003). Euler's totient φ(1003) = 928 numbers up to 1003 share no factor with it.
- 4
The digits of 1003 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1003 = 17 \times 59 \]
1003 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1080 |
| Euler totient φ(n) | 928 |
| Square | 1006009 |
| Cube | 1009027027 |
| Square root | 31.670175 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 41 |
| Scientific notation | 1.003 × |
1003 in other forms
| Form | Value |
|---|---|
| In words | one thousand and three |
| Roman numerals | MIII |
| Binary (base 2) | 1111101011 |
| Octal (base 8) | 1753 |
| Hexadecimal (base 16) | 3EB |
| Base 3 | 1101011 |
| As time | 1003 seconds = 16 min 43 s |
Is 1003 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 | 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 | 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 2) | 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 1003 a prime number?
No. 1003 = 17 × 59, so it is divisible by 17.
What are the factors of 1003?
1, 17, 59, 1003.
What is 1003 in binary?
1111101011 (hexadecimal 3EB, octal 1753).
What is the square root of 1003?
About 31.6702.
What is 1003 in Roman numerals?
MIII.
Is 1003 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 1003?
1003 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 17 × 59, the product of two primes.