Is 75 Prime?

Check if 75 is a prime number. A prime number is only divisible by 1 and itself.

Is prime?
Result: ✗ NO — 75 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 75 is prime, we need to verify that no number from 2 to √75 divides it evenly.

Step 2 Determine Testing Range

Since 75 is odd, we only need to check odd divisors.


We only need to test up to √75 ≈ 8.66, which rounds down to 8.


If 75 has a factor larger than √75, it must also have a corresponding factor smaller than √75.

Step 3 Test Odd Divisors

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


75 ÷ 3 = 25 (no remainder!)

We found that 3 divides 75 evenly!

Step 4 Conclusion
75 = 3 × 25

Since 75 has factors other than 1 and itself, 75 is NOT a prime number.