# Is 83 prime or composite?

#### Understand the Problem

The question is asking whether the number 83 is a prime or composite number. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, while a composite number can be divided by numbers other than 1 and itself. We will determine the nature of 83 by checking its divisibility.

83 is a prime number.

The final answer is that 83 is a prime number.

#### Steps to Solve

1. Check if 83 is divisible by 2, the smallest prime

83 is an odd number, so it is not divisible by 2.

2. Check if 83 is divisible by 3

Sum of the digits of 83 is $8 + 3 = 11$. Since 11 is not divisible by 3, 83 is not divisible by 3.

3. Check if 83 is divisible by 5

Since 83 does not end in 0 or 5, it is not divisible by 5.

4. Check if 83 is divisible by other prime numbers up to \sqrt{83}

$\sqrt{83} \approx 9.11$, thus we need to check divisibility by 7.

83 divided by 7 equals approximately 11.86, which is not an integer, so 83 is not divisible by 7.

5. Conclusion

Since 83 is not divisible by any prime number less than or equal to its square root, it is a prime number.

The final answer is that 83 is a prime number.