Is 109 Prime?
Check if 109 is a prime number. A prime number is only divisible by 1 and itself.
Result:
✓ YES — 109 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 109 is prime, we need to verify that no number from 2 to √109 divides it evenly.
Step 2
Determine Testing Range
Since 109 is odd, we only need to check odd divisors.
We only need to test up to √109 ≈ 10.44, which rounds down to 10.
If 109 has a factor larger than √109, it must also have a corresponding factor smaller than √109.
Step 3
Test Odd Divisors
Testing: 3, 5, 7, ... up to 10
109 ÷ 3 = 36 remainder 1
109 ÷ 5 = 21 remainder 4
109 ÷ 7 = 15 remainder 4
109 ÷ 9 = 12 remainder 1
None of these numbers divide 109 evenly.
Step 4
Conclusion
109 has no divisors between 2 and 10.
The only factors of 109 are 1 and 109 itself.
Therefore, 109 is a PRIME number!