Is 105 Prime?
Check if 105 is a prime number. A prime number is only divisible by 1 and itself.
Result:
✗ NO — 105 is NOT 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 105 is prime, we need to verify that no number from 2 to √105 divides it evenly.
Step 2
Determine Testing Range
Since 105 is odd, we only need to check odd divisors.
We only need to test up to √105 ≈ 10.25, which rounds down to 10.
If 105 has a factor larger than √105, it must also have a corresponding factor smaller than √105.
Step 3
Test Odd Divisors
Testing: 3, 5, 7, ... up to 10
105 ÷ 3 = 35 (no remainder!)
We found that 3 divides 105 evenly!
Step 4
Conclusion
105 = 3 × 35
Since 105 has factors other than 1 and itself, 105 is NOT a prime number.