Question

these are statements about factors and prime and composite numbers.
which statements are true? check all that apply.

the numbers 4, 9, 25, and 49 are composite numbers.
the number 1 is a prime number.
the first prime number is 2.
a composite number can be written as the product of prime numbers.

Explanation:

Analyze statement 1

The numbers 4, 9, 25, and 49 each have more than two factors:
\(4 = 1 \times 4, 2 \times 2\) (factors: 1, 2, 4)
\(9 = 1 \times 9, 3 \times 3\) (factors: 1, 3, 9)
\(25 = 1 \times 25, 5 \times 5\) (factors: 1, 5, 25)
\(49 = 1 \times 49, 7 \times 7\) (factors: 1, 7, 49)
Since they have more than two factors, they are composite. This statement is true.

Analyze statements 2 and 3

By definition, a prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.
The number 1 has only one factor (1), so it is neither prime nor composite. Statement 2 is false.
The smallest and first prime number is 2, as its only factors are 1 and 2. Statement 3 is true.

Analyze statement 4

According to the Fundamental Theorem of Arithmetic, every composite number can be uniquely factored into a product of prime numbers (its prime factorization). This statement is true.

Answer:

• The numbers 4, 9, 25, and 49 are composite numbers. (Correct answer)
• The number 1 is a prime number.
• The first prime number is 2. (Correct answer)
• A composite number can be written as the product of prime numbers. (Correct answer)