A composite number is a positive integer that has at least one positive divisor other than 1 or the number itself. In other words, a composite number can be expressed as a product of two or more smaller integers.
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All composite numbers are non-prime, meaning they have at least one positive divisor other than 1 and the number itself.
The smallest composite number is 4, as it can be expressed as the product of 2 and 2.
Examples of composite numbers include 6 (2 x 3), 8 (2 x 4), 9 (3 x 3), and 10 (2 x 5).
Composite numbers have more factors than prime numbers, and their factors can be found by factoring the number.
Identifying composite numbers is important for understanding concepts like prime factorization, which is used in many mathematical applications.
Review Questions
How can you determine if a number is a composite number?
To determine if a number is a composite number, you need to check if it has any positive divisors other than 1 and the number itself. If the number can be expressed as a product of two or more smaller integers, then it is a composite number. For example, the number 6 is a composite number because it can be written as 2 x 3, which means it has divisors other than 1 and 6.
Explain the relationship between composite numbers and factors.
Composite numbers are closely related to factors. By definition, a composite number has at least one positive divisor other than 1 and the number itself. These divisors are the factors of the composite number. For instance, the number 12 is a composite number because it has factors such as 1, 2, 3, 4, 6, and 12. Understanding the factors of a composite number is important for finding its prime factorization and working with concepts like multiples and divisibility.
Describe how the concept of composite numbers is used in the context of finding multiples and factors.
The concept of composite numbers is essential for understanding the topics of finding multiples and factors. Composite numbers, by definition, can be expressed as a product of two or more smaller integers. This means that composite numbers have more factors than prime numbers, and their factors can be found by factoring the number. Additionally, the multiples of a composite number can be determined by multiplying the number by various integers. Recognizing the composite nature of a number can help you efficiently identify its factors and multiples, which are fundamental concepts in pre-algebra.