Is 133 Prime?

Check if 133 is a prime number. A prime number is only divisible by 1 and itself.

Result: ✗ NO — 133 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 133 is prime, we need to verify that no number from 2 to √133 divides it evenly.

Step 2 Determine Testing Range

Since 133 is odd, we only need to check odd divisors.

We only need to test up to √133 ≈ 11.53, which rounds down to 11.

If 133 has a factor larger than √133, it must also have a corresponding factor smaller than √133.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 11

133 ÷ 3 = 44 remainder 1

133 ÷ 5 = 26 remainder 3

133 ÷ 7 = 19 (no remainder!)

We found that 7 divides 133 evenly!

Step 4 Conclusion

133 = 7 × 19

Since 133 has factors other than 1 and itself, 133 is NOT a prime number.