Write a factor for each of the following numbers and indicate if it is a prime or composite number. | Number | Factors | Prime or Composite | |---|---|---| | 8 | 1, 2, 4, 8 | Composite | | 25 | 1, 5, 25 | Composite | | 21 | 1, 3, 7, 21 | Composite | | 30 | 1, 2, 3, 5, 6, 10, 15, 30 | Composite | | 5 | 1, 5 | Prime | | 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | Composite | | 19 | 1, 19 | Prime | | 12 | 1, 2, 3, 4, 6, 12 | Composite |

To determine whether a number is prime or composite, first recognize the definitions:

Prime Number: A number greater than 1 that has no divisors other than 1 and itself.
Composite Number: A number greater than 1 that has more than two divisors.

Let’s look at each number provided and verify their factors:

8:

Factors: 1, 2, 4, 8
Since 8 has more than two factors, it is a composite number.


25:

Factors: 1, 5, 25
Because 25 has more than two factors, it is a composite number.


21:

Factors: 1, 3, 7, 21
As it has more than two factors, 21 is a composite number.


30:

Factors: 1, 2, 3, 5, 6, 10, 15, 30
With multiple factors, 30 is a composite number.


5:

Factors: 1, 5
Since 5 has only two factors, it is a prime number.


48:

Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Given its multiple factors, 48 is a composite number.


19:

Factors: 1, 19
With just two factors, 19 is a prime number.


12:

Factors: 1, 2, 3, 4, 6, 12
As it has more than two factors, 12 is a composite number.



In summary, a number is classified based on its divisors: numbers with only two distinct divisors (1 and itself) are prime, while those with more than two divisors are composite.

Answered by ElijahBenjaminCarter | 2025-07-21