Is 93 a prime or composite number? This question often arises in discussions about number theory and the classification of integers. To answer this question, we need to delve into the definition of prime and composite numbers and apply them to the number 93.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and itself. On the other hand, a composite number is a natural number greater than 1 that has at least one positive divisor other than 1 and itself. This means that a composite number can be divided evenly by at least one number other than 1 and itself.
To determine whether 93 is prime or composite, we need to check if there are any numbers between 2 and 92 (since 1 is not a valid divisor) that can divide 93 evenly. If we find such a number, then 93 is composite; otherwise, it is prime.
Let’s start by checking the divisibility of 93 by the smallest prime number, 2. Since 93 is an odd number, it is not divisible by 2. Next, we can check divisibility by the next prime number, 3. The sum of the digits of 93 is 9 + 3 = 12, which is divisible by 3. Therefore, 93 is divisible by 3, making it a composite number.
Now that we have determined that 93 is a composite number, we can also find its factors. The prime factorization of 93 is 3 × 31. This means that 93 can be divided evenly by both 3 and 31. In conclusion, 93 is a composite number with prime factors 3 and 31.
