Topic 7 Review

A

100

True or False: 8 has more than three factors.

True.

The factors of 8 are:
1, 2, 4, and 8.

Since 8 has four factors, it has more than three factors.

200

If 4 is a multiple of a number, what could that number be?

If 4 is a multiple of a number, that number could be any factor of 4.

The factors of 4 are:
1, 2, and 4.

So, the number could be 1, 2, or 4.

300

Sarah has 24 apples and wants to divide them equally into bags.How many different combinations of apples can Sarah make when dividing 24 apples equally into bags?

The answer is 8 combinations.

• 1 apple per bag: She would need 24 bags.
• 2 apples per bag: She would need 12 bags.
• 3 apples per bag: She would need 8 bags.
• 4 apples per bag: She would need 6 bags.
• 6 apples per bag: She would need 4 bags.
• 8 apples per bag: She would need 3 bags.
• 12 apples per bag: She would need 2 bags.
• 24 apples per bag: She would need 1 bag.

400

A gardener has 60 plants and needs to arrange them in rows for a garden show. She wants each row to contain a prime number of plants. What are the possible prime numbers of plants she can have in each row, and how many rows will she need for each arrangement?

The possible prime numbers of plants in each row are 2, 3, and 5, with the corresponding number of rows being:

• 30 rows for 2 plants per row
• 20 rows for 3 plants per row
• 12 rows for 5 plants per row

B

100

What are the first three multiples of 5?

The first three multiples of 5 are:

5, 10, and 15.

200

List all the composite numbers between 10 and 20

 

The composite numbers between 10 and 20 are:

12, 14, 15, 16, 18, and 20.

300

Emily is organizing a charity event and needs to distribute 48 gift items into gift bags. She wants each bag to contain the same number of items, and she wants to use the highest possible number of items per bag, without putting all 48 items in one bag. What is the largest number of items she can put in each bag, and how many bags will she need?

To solve the problem, we need to find the highest number of items Emily can put in each bag without using all 48 items in one bag.

The factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Since the problem specifies not using all 48 items in one bag, the highest number of items she can put in each bag is 24.

If she puts 24 items in each bag, she will need:

400

A teacher has 36 pencils and wants to organize them into boxes for a class project. She needs to arrange the pencils in such a way that each box contains a number of pencils that is either a prime number or a composite number with exactly four factors. What are the possible numbers of pencils she can put in each box, and how many boxes will she need for each arrangement?

The possible numbers of pencils per box are 2, 3, and 6, with the following number of boxes for each arrangement:

• 18 boxes for 2 pencils per box.
• 12 boxes for 3 pencils per box.
• 6 boxes for 6 pencils per box.

C

100

True or False: 1 is a prime number.

False.

A prime number is defined as a number greater than 1 that has exactly two distinct positive factors: 1 and itself.

Since 1 only has one factor (itself), it is not a prime number.

200

 True or False: All even numbers are composite.

While most even numbers are composite, there is one exception: 2.

Explanation:

• An even number is divisible by 2.
• A composite number has more than two factors.
• 2 is even, but it has exactly two factors: 1 and 2, making it a prime number, not composite.

All other even numbers greater than 2 are composite because they have at least three factors: 

D

100

What is the 6th multiple of 3?

To find the 6th multiple of 3, multiply 3 by 6:

3×6=18 

The 6th multiple of 3 is 18.

200

What is the smallest composite number?

The smallest composite number is 4.