The smallest composite number is ______.

(a) 2

(b) 4

(c) 1

(d) None of these

The smallest composite number is (b) 4. To understand why, let’s break down what composite numbers are and how they differ from other types of numbers.

Defining Composite Numbers

A composite number is defined as a positive integer that has at least one positive divisor other than one and itself. In simpler terms, it means that a composite number can be divided evenly by numbers other than just 1 and itself.

Examples of Composite Numbers

• 4: The divisors are 1, 2, and 4. Since it can be divided by 2 (which is neither 1 nor 4), it is composite.
• 6: The divisors are 1, 2, 3, and 6. It can be divided by 2 and 3, making it composite.
• 8: The divisors are 1, 2, 4, and 8. Again, it is composite because it can be divided by 2 and 4.

Understanding Other Options

Now, let’s look at the other options provided:

• 2: This is a prime number because its only divisors are 1 and 2.
• 1: This is neither prime nor composite. It has only one positive divisor, which is itself.
• None of these: This option is incorrect because we have identified 4 as the smallest composite number.

Why 4 is the Smallest Composite Number

When we list the positive integers starting from 1, we have:

• 1 (not composite)
• 2 (prime)
• 3 (prime)
• 4 (composite)

As you can see, 4 is the first number in this sequence that meets the criteria for being composite. It has divisors other than just 1 and itself, specifically 2.

Conclusion

In summary, the smallest composite number is 4, as it is the first integer that can be divided by numbers other than 1 and itself. Understanding the definitions and characteristics of different types of numbers helps clarify why 4 fits the definition of a composite number, while the others do not.