Is 1003 prime?

Steps to Solve

1. 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.

2. 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 ).

3. 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.

4. 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.