Is 103 Prime?
Check if 103 is a prime number. A prime number is only divisible by 1 and itself.
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!