Factors and Multiples!

Multiples of a Number

100

List the multiples of 3 from 1 to 30.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

200

Tyler wants to build a rectangle with an area of 20 square units using square tiles. 

Can Tyler build a rectangle with a width of 4 units? Explain or show your reasoning.

Yes, a rectangle with a width of 4 units and a length of 5 units has 20 square units in it.

300

Tyler wants to build a rectangle with an area of 20 square units using square tiles.

Can Tyler build a rectangle with a width of 6 units? Explain or show your reasoning.

No, if the width is 6 and the length is 3, that means using 18 square tiles. If the length is 4, that means using 24 square tiles.

400

Select all numbers that are multiples of 8.

16  28  40  54  66  72  84  96

16

40

72

96

Factors and Factor Pairs

100

What are the possible side lengths of a rectangle with area 10 square units?

2 units by 5 units, or 1 unit by 10 units

200

List the possible whole-number side lengths of rectangles with an area of 32 square units. Explain or show how you know your list is complete.

1 unit by 32 units, 2 units by 16 units, 4 units by 8 units. Those are all of the possible rectangles because there are no other factors of 32.

300

List the factors of 15.

1, 3, 5, 15

400

Find the factor pairs of 36. How many factors does 36 have?

1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. 

9 factors

Prime and Composite

100

List the factor pairs of 37. Is it prime or composite? How do you know?

Prime, because the only factor pair is 1 and 37.

200

List the factor pairs of 27. Is it prime or composite? How do you know?

Composite, because it has the factor pairs 1 and 27 and also 3 and 9.

300

List the factor pairs of 77. Is it prime or composite? How do you know?

Composite, because it has the factor pairs 1 and 77 and also 7 and 11.

400

What is the largest prime number you can find? Explain or show why it is a prime number.

97 is prime because its only factor pair is 1 and 97. I tried all of the other numbers and could not find another factor pair.

Story Problems

100

You want to arrange all 18 students in your class in equal rows. 

How many rows can you have? How many students would be in each row?

6 rows of 3

3 rows of 6

9 rows of 2

2 rows of 9 

1 row of 18

18 rows of 1

200

Pens are sold in packages of 5 and also in packages of 6.  Jada wants to buy 60 pens for her class. Which packages of pens and how many should Jada buy if she doesn't want any extras? Explain or show your reasoning.

• 10 packages of 6 pens, because 10 x 6 =60. That is fewer packages than 12 packages of 5.
• 12 packages of 5 pens, because her classmates are seated in groups of 5.

300

Pens are sold in packages of 5 and also in packages of 6. Han wants to buy 55 pens for his class. Which packages of pens and how many should Han buy? Explain or show your reasoning.

• 11 packages of 5 pens, because 11 x 5 =55.
• 10 packages of 6 pens because 10 x 6 =60 . He will have 5 extra pens.

400

Each package of burgers has 8 burgers. Each package of burger buns has 12 buns. Westley expects to need 60 burgers for a class picnic.

How many packages of burgers should Lin get? Explain or show your reasoning.

Can Westley get exactly 60 burger buns? How many packages of burger buns should Lin get? Explain or show your reasoning.

Lin should get 8 packages of burgers because 8 x 8 = 64.  He will have 4 extra.  If he got 7 packages, he would only have 56 burgers, and that is not enough.

Yes, Westley can get 60 burger buns.  If he got 5 packages that would be 5 x 12 = 60 because 5 x 10 is 50 and 5 x 2 =10. 50 + 10 = 60.