Is 103 Prime?

Check if 103 is a prime number. A prime number is only divisible by 1 and itself.

Is prime?
Result: ✓ YES — 103 is a prime number
Step-by-Step Solution
Step 1 What is a Prime Number?

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.


To check if 103 is prime, we need to verify that no number from 2 to √103 divides it evenly.

Step 2 Determine Testing Range

Since 103 is odd, we only need to check odd divisors.


We only need to test up to √103 ≈ 10.15, which rounds down to 10.


If 103 has a factor larger than √103, it must also have a corresponding factor smaller than √103.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 10


103 ÷ 3 = 34 remainder 1
103 ÷ 5 = 20 remainder 3
103 ÷ 7 = 14 remainder 5
103 ÷ 9 = 11 remainder 4

None of these numbers divide 103 evenly.

Step 4 Conclusion

103 has no divisors between 2 and 10.


The only factors of 103 are 1 and 103 itself.


Therefore, 103 is a PRIME number!