Is 65 Prime?

Check if 65 is a prime number. A prime number is only divisible by 1 and itself.

Result: ✗ NO — 65 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 65 is prime, we need to verify that no number from 2 to √65 divides it evenly.

Step 2 Determine Testing Range

Since 65 is odd, we only need to check odd divisors.

We only need to test up to √65 ≈ 8.06, which rounds down to 8.

If 65 has a factor larger than √65, it must also have a corresponding factor smaller than √65.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 8

65 ÷ 3 = 21 remainder 2

65 ÷ 5 = 13 (no remainder!)

We found that 5 divides 65 evenly!

Step 4 Conclusion

65 = 5 × 13

Since 65 has factors other than 1 and itself, 65 is NOT a prime number.