Prime and Composite Numbers

A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite. The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 since each of these numbers has only two factors,1 and itself.

When the area of a rectangle is a prime number, there is only one set of possible dimensions for that rectangle. When the area of a rectangle is a composite number, there are two or more sets of possible dimensions for that rectangle. Each set of dimensions is a pair of factors.

To determine if a number is prime or composite, follow these steps:

Illustration 1: Is the number 2 prime or composite?

Solution: The factors of 2 are 1 , and 2. Hence,  2 is prime.

Illustration 2: Is the number 9 prime or composite?

Solution: The factors of 9 are 1 x 9, 3 x 3. Hence, 9 is composite.

Illustration 3: Find the composite numbers which are multiple of 5 and less than 30.

Solution: As multiples of 5 which are less than 30 are 5, 10, 15, 20, 25

Now, factors of 5 = 1,5

  factors of 10 = 1, 2, 5, 10

  factors of  15 = 1, 3, 5, 15

  factors of 20 = 1, 2 , 4, 5 , 10, 20

  factors of  25 = 1, 5, 25

As 10, 15,20, 25 has more than 2 factors, Hence all these numbers are composite.

But 5 has only two factors, so 5 is prime.

Hence, the composite numbers which are multiple of 5 and less than 30 are 10, 15, 20, 25