Question

1. which of these is a prime number? a. 39 b. 97 c. 55 d. 63 1, 3, 7, 9, 21, 63 2. which of these is a composite number? select two correct answers. a. 2 b. 4 c. 19 d. 23 e. 32 3. which model shows a composite number of hearts? circle two correct answers.

Explanation:

Step1: Recall prime - composite definitions

A prime number has only two distinct positive divisors: 1 and itself. A composite number has more than two positive divisors.

Step2: Analyze question 1

• For 39: $39=3\times13$, so it has factors 1, 3, 13, 39 and is composite.
• For 97: Its only positive divisors are 1 and 97, so it is prime.
• For 55: $55 = 5\times11$, so it has factors 1, 5, 11, 55 and is composite.
• For 63: $63=3\times21 = 7\times9$, so it has factors 1, 3, 7, 9, 21, 63 and is composite.

Step3: Analyze question 2

• For 2: Its only positive divisors are 1 and 2, so it is prime.
• For 4: $4 = 2\times2$, so it has factors 1, 2, 4 and is composite.
• For 19: Its only positive divisors are 1 and 19, so it is prime.
• For 23: Its only positive divisors are 1 and 23, so it is prime.
• For 32: $32=2\times16=4\times8$, so it has factors 1, 2, 4, 8, 16, 32 and is composite.

Step4: Analyze question 3

Count the number of hearts in each model. The first model has 7 hearts, 7 is prime as its only divisors are 1 and 7. The second model has 4 hearts, $4 = 2\times2$ (composite). The third model has 1 heart (neither prime nor composite by convention). The fourth model has 8 hearts, $8=2\times4$ (composite). The fifth model has 2 hearts, 2 is prime.

Answer:

1. B. 97
2. B. 4, E. 32
3. Second model (4 hearts), Fourth model (8 hearts)