What is a prime number in math?

A prime number is a natural number greater than 1 that is divisible only by 1 and itself, meaning it has no other divisors. In simpler terms, a prime number cannot be evenly divided by any other number except 1 and itself.

For example, the number 2 is the smallest prime number because it is only divisible by 1 and 2. Similarly, 3, 5, 7, 11, 13, and so on are prime numbers because they cannot be divided by any other numbers except 1 and themselves.

On the other hand, numbers that have divisors other than 1 and themselves are called composite numbers. For instance, 4 is a composite number because it can be divided evenly by 1, 2, and 4.

Prime numbers have unique properties and play a fundamental role in number theory and various branches of mathematics. They are the building blocks of all positive integers, and their distribution and properties have been subjects of study for mathematicians for centuries. Prime numbers also have practical applications in cryptography, algorithms, and computer science.

What is a composite number?

A non-prime number, also known as a composite number, is a natural number greater than 1 that has divisors other than 1 and itself. In other words, a non-prime number can be divided evenly by at least one number other than 1 and itself.

For example, the number 4 is a non-prime number because it can be divided evenly by 1, 2, and 4. Similarly, numbers like 6, 8, 9, 10, 12, and so on are all composite numbers because they have divisors other than 1 and themselves.

Composite numbers can have multiple factors or divisors. For instance, 6 has divisors 1, 2, 3, and 6. 8 has divisors 1, 2, 4, and 8. 9 has divisors 1, 3, and 9. The number of divisors can vary for different composite numbers.

It’s worth noting that 1 is not considered a prime number nor a composite number because it does not meet the criteria for either category. It is a unique number that only has one positive divisor, which is 1 itself.

In contrast to prime numbers, composite numbers have a broader range of divisors, and they are composed of prime factors. Understanding composite numbers is important in various mathematical concepts, including factorization, multiplication, and the study of divisibility rules.