Is 127 Prime?

Check if 127 is a prime number. A prime number is only divisible by 1 and itself.

Is prime?
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!