Is 73 Prime?
Check if 73 is a prime number. A prime number is only divisible by 1 and itself.
Result:
✓ YES — 73 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 73 is prime, we need to verify that no number from 2 to √73 divides it evenly.
Step 2
Determine Testing Range
Since 73 is odd, we only need to check odd divisors.
We only need to test up to √73 ≈ 8.54, which rounds down to 8.
If 73 has a factor larger than √73, it must also have a corresponding factor smaller than √73.
Step 3
Test Odd Divisors
Testing: 3, 5, 7, ... up to 8
73 ÷ 3 = 24 remainder 1
73 ÷ 5 = 14 remainder 3
73 ÷ 7 = 10 remainder 3
None of these numbers divide 73 evenly.
Step 4
Conclusion
73 has no divisors between 2 and 8.
The only factors of 73 are 1 and 73 itself.
Therefore, 73 is a PRIME number!