Is 67 a Composite Number- Unraveling the Mathematical Mystery of Prime and Composite Numbers

Is 67 a composite number? This question often arises when discussing the classification of numbers in mathematics. To answer this question, we need to understand what a composite number is and how it differs from prime numbers.

In mathematics, a composite number is a positive integer greater than 1 that is not prime. 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 by 1 and itself without leaving a remainder. On the other hand, a composite number has at least one positive divisor other than 1 and itself.

To determine whether 67 is a composite number, we must check if it has any divisors other than 1 and itself. By performing the prime factorization of 67, we can identify its divisors. Prime factorization is the process of expressing a number as a product of prime numbers.

Let’s start by dividing 67 by the smallest prime number, which is 2. Since 67 is not divisible by 2, we move on to the next prime number, which is 3. We continue this process until we find a prime number that divides 67 or until we reach the square root of 67.

After trying various prime numbers, we find that 67 is not divisible by any prime numbers other than itself. Therefore, 67 has no divisors other than 1 and itself, making it a prime number, not a composite number.

In conclusion, the answer to the question “Is 67 a composite number?” is no. 67 is a prime number, as it has no divisors other than 1 and itself. This distinction between prime and composite numbers is essential in understanding the properties and applications of numbers in various mathematical fields.