Select The Best Answer For The Question.18. Which Of The Following Is A Composite Number?A. 19 B. 1 C. 63 D. 0

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What are Composite Numbers?

In mathematics, a composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, it is a number that is not a prime number. Composite numbers are the building blocks of mathematics, and understanding them is essential for solving various mathematical problems.

Definition of Composite Numbers

A composite number is defined as a positive integer that can be expressed as the product of two smaller positive integers. For example, 6 is a composite number because it can be expressed as 2 x 3. Similarly, 12 is a composite number because it can be expressed as 2 x 2 x 3.

Examples of Composite Numbers

Some examples of composite numbers include:

  • 4 (2 x 2)
  • 6 (2 x 3)
  • 8 (2 x 4)
  • 9 (3 x 3)
  • 10 (2 x 5)
  • 12 (2 x 2 x 3)

Why are Composite Numbers Important?

Composite numbers are important in mathematics because they are used to solve various mathematical problems. For example, in algebra, composite numbers are used to solve quadratic equations. In geometry, composite numbers are used to find the area and perimeter of shapes.

How to Identify Composite Numbers

To identify composite numbers, we need to check if the number has any divisors other than one or itself. We can do this by dividing the number by all the integers from 2 to the square root of the number. If the number is divisible by any of these integers, then it is a composite number.

Solving the Problem

Now, let's solve the problem: Which of the following is a composite number?

A. 19 B. 1 C. 63 D. 0

To solve this problem, we need to check if each of the options is a composite number.

  • Option A: 19 is a prime number because it has no divisors other than one and itself.
  • Option B: 1 is not a composite number because it has no divisors other than one.
  • Option C: 63 is a composite number because it can be expressed as 7 x 9.
  • Option D: 0 is not a composite number because it has no divisors other than zero.

Therefore, the correct answer is:

C. 63

Conclusion

In conclusion, composite numbers are an essential part of mathematics. They are used to solve various mathematical problems, and understanding them is crucial for success in mathematics. By identifying composite numbers, we can solve problems in algebra, geometry, and other areas of mathematics.

Key Takeaways

  • Composite numbers are positive integers that have at least one positive divisor other than one or itself.
  • Composite numbers can be expressed as the product of two smaller positive integers.
  • Examples of composite numbers include 4, 6, 8, 9, 10, and 12.
  • Composite numbers are used to solve various mathematical problems.
  • To identify composite numbers, we need to check if the number has any divisors other than one or itself.

Further Reading

If you want to learn more about composite numbers, I recommend checking out the following resources:

  • Khan Academy: Composite Numbers
  • Math Is Fun: Composite Numbers
  • Wikipedia: Composite Number

References

  • "Algebra" by Michael Artin
  • "Geometry" by Michael Spivak
  • "Number Theory" by Ivan Niven
    Composite Numbers Q&A =========================

Frequently Asked Questions about Composite Numbers

Q: What is a composite number?

A: A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, it is a number that is not a prime number.

Q: How do I identify a composite number?

A: To identify a composite number, you need to check if the number has any divisors other than one or itself. You can do this by dividing the number by all the integers from 2 to the square root of the number. If the number is divisible by any of these integers, then it is a composite number.

Q: What are some examples of composite numbers?

A: Some examples of composite numbers include:

  • 4 (2 x 2)
  • 6 (2 x 3)
  • 8 (2 x 4)
  • 9 (3 x 3)
  • 10 (2 x 5)
  • 12 (2 x 2 x 3)

Q: Why are composite numbers important?

A: Composite numbers are important in mathematics because they are used to solve various mathematical problems. For example, in algebra, composite numbers are used to solve quadratic equations. In geometry, composite numbers are used to find the area and perimeter of shapes.

Q: Can a composite number be a prime number?

A: No, a composite number cannot be a prime number. By definition, a composite number is a number that has at least one positive divisor other than one or itself, while a prime number is a number that has only two divisors: one and itself.

Q: Is zero a composite number?

A: No, zero is not a composite number. Zero has no divisors other than zero itself, so it does not meet the definition of a composite number.

Q: Is one a composite number?

A: No, one is not a composite number. One has no divisors other than one itself, so it does not meet the definition of a composite number.

Q: Can a composite number be a perfect square?

A: Yes, a composite number can be a perfect square. For example, 4 is a composite number (2 x 2) and a perfect square (2^2).

Q: Can a composite number be a perfect cube?

A: Yes, a composite number can be a perfect cube. For example, 8 is a composite number (2 x 4) and a perfect cube (2^3).

Q: How do I find the prime factorization of a composite number?

A: To find the prime factorization of a composite number, you need to break down the number into its prime factors. You can do this by dividing the number by prime numbers starting from 2 until you reach the square root of the number.

Q: What is the difference between a composite number and a multiple?

A: A composite number is a number that has at least one positive divisor other than one or itself, while a multiple is a number that is the product of a number and an integer. For example, 6 is a composite number (2 x 3), while 12 is a multiple of 6 (6 x 2).

Q: Can a composite number be a multiple of a prime number?

A: Yes, a composite number can be a multiple of a prime number. For example, 6 is a composite number (2 x 3) and a multiple of the prime number 3.

Q: Can a composite number be a multiple of a composite number?

A: Yes, a composite number can be a multiple of a composite number. For example, 12 is a composite number (2 x 2 x 3) and a multiple of the composite number 6 (2 x 3).

Conclusion

In conclusion, composite numbers are an essential part of mathematics. They are used to solve various mathematical problems, and understanding them is crucial for success in mathematics. By identifying composite numbers, we can solve problems in algebra, geometry, and other areas of mathematics.

Key Takeaways

  • Composite numbers are positive integers that have at least one positive divisor other than one or itself.
  • Composite numbers can be expressed as the product of two smaller positive integers.
  • Examples of composite numbers include 4, 6, 8, 9, 10, and 12.
  • Composite numbers are used to solve various mathematical problems.
  • To identify composite numbers, we need to check if the number has any divisors other than one or itself.

Further Reading

If you want to learn more about composite numbers, I recommend checking out the following resources:

  • Khan Academy: Composite Numbers
  • Math Is Fun: Composite Numbers
  • Wikipedia: Composite Number

References

  • "Algebra" by Michael Artin
  • "Geometry" by Michael Spivak
  • "Number Theory" by Ivan Niven