Understanding Composite Numbers: Properties and Examples

Composite numbers

Whole numbers that have more than two factors

Composite numbers are positive integers that have more than two factors. In other words, composite numbers can be divided evenly by more than just 1 and itself. For example, 6 is a composite number because it can be evenly divided by 1, 2, 3, and 6. On the other hand, prime numbers are positive integers that have only two factors, 1 and itself. For example, 7 is a prime number because it has only two factors, 1 and 7.

The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20. It’s important to remember that 1 is not a composite number, because it has only one factor.

Composite numbers have several properties that are worth noting. Firstly, they can always be expressed as the product of prime factors. This is known as the fundamental theorem of arithmetic. For example, the composite number 36 can be expressed as 2 x 2 x 3 x 3, where 2 and 3 are prime factors. This is the only way to write 36 as the product of prime numbers.

Another property of composite numbers is that they have a specific number of factors. A composite number with exactly three factors is the square of a prime number. For example, 9 is a composite number with only three factors (1, 3, and 9), and it’s the square of the prime number 3. A composite number with exactly four factors is the product of two distinct prime numbers. For example, 15 is a composite number with four factors (1, 3, 5, and 15), and it’s the product of the distinct prime numbers 3 and 5.

In conclusion, composite numbers are important in number theory and have many interesting properties. They can always be expressed as the product of prime factors and have a specific number of factors based on whether they are the square of a prime number or the product of two distinct prime numbers.

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