Is 90 a prime number? This question often arises in the realm of mathematics, particularly when discussing prime numbers and their properties. Prime numbers are a fundamental concept in number theory, and understanding whether 90 is a prime number can provide valuable insights into the nature of numbers and their divisibility.
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. In other words, a prime number cannot be formed by multiplying two smaller natural numbers. The first few prime numbers are 2, 3, 5, 7, 11, and so on. These numbers are essential building blocks in mathematics, as they are the only numbers that cannot be expressed as the product of two smaller natural numbers.
To determine if 90 is a prime number, we must examine its factors. A factor of a number is a number that divides the given number without leaving a remainder. If a number has more than two factors, it is not a prime number. In the case of 90, we can start by checking if it is divisible by any of the smaller prime numbers, such as 2, 3, 5, or 7.
Upon dividing 90 by 2, we find that it is divisible, resulting in a quotient of 45. This means that 2 is a factor of 90. Since 90 is divisible by 2, it cannot be a prime number, as prime numbers have exactly two distinct positive divisors: 1 and the number itself. Moreover, since 90 is an even number, it is not a prime number, as all prime numbers are odd, except for the number 2.
Furthermore, we can continue checking for other factors. Dividing 90 by 3 yields a quotient of 30, which means that 3 is also a factor of 90. Similarly, dividing 90 by 5 gives us a quotient of 18, indicating that 5 is another factor. We can see that 90 has multiple factors, including 2, 3, 5, 6, 9, 10, 15, 18, 30, and 45.
In conclusion, 90 is not a prime number because it has more than two factors. This demonstrates the importance of prime numbers in mathematics and their unique properties. By understanding the nature of prime numbers, we can better appreciate the underlying structure of numbers and their divisibility.
