Is 17 Prime?

Check if 17 is a prime number. A prime number is only divisible by 1 and itself.

Result: ✓ YES — 17 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 17 is prime, we need to verify that no number from 2 to √17 divides it evenly.

Step 2 Determine Testing Range

Since 17 is odd, we only need to check odd divisors.

We only need to test up to √17 ≈ 4.12, which rounds down to 4.

If 17 has a factor larger than √17, it must also have a corresponding factor smaller than √17.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 4

17 ÷ 3 = 5 remainder 2

None of these numbers divide 17 evenly.

Step 4 Conclusion

17 has no divisors between 2 and 4.

The only factors of 17 are 1 and 17 itself.

Therefore, 17 is a PRIME number!