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.
Answer
83 is a prime number.
Answer for screen readers
The final answer is that 83 is a prime number.
Steps to Solve
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Check if 83 is divisible by 2, the smallest prime
83 is an odd number, so it is not divisible by 2.
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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.
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Check if 83 is divisible by 5
Since 83 does not end in 0 or 5, it is not divisible by 5.
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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.
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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.
More Information
Prime numbers have many important applications in number theory and cryptography.
Tips
A common mistake is not checking divisibility by all prime numbers up to the square root of the given number.
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