Is 127 Prime?
Check if 127 is a prime number. A prime number is only divisible by 1 and itself.
Result:
✓ YES — 127 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 127 is prime, we need to verify that no number from 2 to √127 divides it evenly.
Step 2
Determine Testing Range
Since 127 is odd, we only need to check odd divisors.
We only need to test up to √127 ≈ 11.27, which rounds down to 11.
If 127 has a factor larger than √127, it must also have a corresponding factor smaller than √127.
Step 3
Test Odd Divisors
Testing: 3, 5, 7, ... up to 11
127 ÷ 3 = 42 remainder 1
127 ÷ 5 = 25 remainder 2
127 ÷ 7 = 18 remainder 1
127 ÷ 9 = 14 remainder 1
127 ÷ 11 = 11 remainder 6
None of these numbers divide 127 evenly.
Step 4
Conclusion
127 has no divisors between 2 and 11.
The only factors of 127 are 1 and 127 itself.
Therefore, 127 is a PRIME number!