Is 1003 prime?
Understand the Problem
The question is asking whether the number 1003 is a prime number. To determine if a number is prime, we check if it is greater than 1 and has no divisors other than 1 and itself.
Answer
No, $1003$ is not a prime number.
Answer for screen readers
No, the number $1003$ is not a prime number.
Steps to Solve
- Check if the number is greater than 1
Since a prime number must be greater than 1, we confirm that ( 1003 > 1 ). This condition is satisfied.
- Find divisors of the number
Next, we need to check if ( 1003 ) can be divided evenly by any numbers other than 1 and itself. We will start checking with prime numbers up to the square root of ( 1003 ) because if it is divisible by any number greater than its square root, the corresponding divisor would have to be smaller than the square root.
The approximate square root of ( 1003 ) is about ( 31.7 ), so we check divisibility by prime numbers up to ( 31 ): ( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 ).
- Check divisibility by each prime number
- Check ( 2 ): ( 1003 ) is odd, so it is not divisible by ( 2 ).
- Check ( 3 ): Sum of digits ( 1 + 0 + 0 + 3 = 4 ), which is not divisible by ( 3 ).
- Check ( 5 ): Last digit is ( 3 ), so not divisible by ( 5 ).
- Check ( 7 ): Calculate ( 1003 \div 7 \approx 143.29 ), not an integer.
- Check ( 11 ): Calculate ( 1003 \div 11 \approx 91.18 ), not an integer.
- Check ( 13 ): Calculate ( 1003 \div 13 = 77.15 ), not an integer.
- Check ( 17 ): Calculate ( 1003 \div 17 \approx 59.00 ), which is an integer.
Since ( 1003 = 17 \times 59 ), ( 1003 ) has divisors other than 1 and itself.
- Conclusion on primality
Since we have found that ( 1003 ) can be divided evenly by ( 17 ) and ( 59 ), we conclude that ( 1003 ) is not a prime number.
No, the number $1003$ is not a prime number.
More Information
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. ( 1003 ) is a composite number because it has divisors other than 1 and itself.
Tips
- Confusing evenness for primality: Some might assume that odd numbers are always prime, but ( 1003 ) is an example of an odd composite number.
- Not checking all primes up to the square root: It's important to verify with all relevant primes to conclude whether a number is prime.
