Is 83 Prime?

Check if 83 is a prime number. A prime number is only divisible by 1 and itself.

Is prime?
Result: ✓ YES — 83 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 83 is prime, we need to verify that no number from 2 to √83 divides it evenly.

Step 2 Determine Testing Range

Since 83 is odd, we only need to check odd divisors.


We only need to test up to √83 ≈ 9.11, which rounds down to 9.


If 83 has a factor larger than √83, it must also have a corresponding factor smaller than √83.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 9


83 ÷ 3 = 27 remainder 2
83 ÷ 5 = 16 remainder 3
83 ÷ 7 = 11 remainder 6
83 ÷ 9 = 9 remainder 2

None of these numbers divide 83 evenly.

Step 4 Conclusion

83 has no divisors between 2 and 9.


The only factors of 83 are 1 and 83 itself.


Therefore, 83 is a PRIME number!