Investigating Factors

Part A.For this part of the activity you will need unifix cubes.

  1. Use 12 cubes and make a 3 by 4 rectangle. The numbers 3 and 4 are called factors of 12. Use the 12 cubes to make a 2 by 6 rectangle. 2 and 6 are also factors of 12. Use the cubes again to make a 1 by 12 rectangle. 1 and 12 are also factors of 12. Record all the factors of 12:

______, ______, ______, ______, ______, ______

  1. Use this method to find all the factors for each of the following numbers:

Number of
Cubes / Factors / Number of
Cubes / Factors
2 / 21
3 / 22
4 / 23
5 / 24
6 / 25
7 / 26
8 / 27
9 / 28
10 / 29
11 / 30
12 / 31
13 / 32
14 / 33
15 / 34
16 / 35
17 / 36
18 / 37
19 / 38
20 / 39
  1. Which numbers have an odd number of factors? What is the special name for these numbers?
  1. How would you write a definition of a prime number and a composite number that uses the idea of multiple-row rectangles?

Part B.Factors and Multiples

  1. Make 3 different rectangles, using 16 cubes for each rectangle. Record below:

_____ by _____, _____ by _____, _____ by _____

The factors of 16 are _____, _____, _____, _____, _____

  1. Make 4 different rectangles, using 24 cubes for each rectangle. Record:

_____ by _____, _____ by _____, _____ by _____, _____ by _____

The factors of 24 are ____, ____, ____, ____, ____, ____, ____, ____, ____

  1. List the factors that 16 and 24 have in common:

_____, _____, _____, _____

Which of these factors is the largest? (GCF) ______

  1. Find the common factors of 15 and 20. Record:

What is the GCF of 15 and 20?

  1. Find the GCF of each pair of numbers:

a)12 and 18 ______b)8 and 12 ______

c)9 and 12 ______d)12 and 24 ______

  1. Make a 4 by 1 rectangle. How man squares are in the rectangle? _____

4 is called a multiple of 4.

Now make a 4 by 2 rectangle. How many squares are in the rectangle? ___

8 is also a multiple of 4.

  1. Make 6 more rectangles with 4 squares on one side. Use the rectangles to find six more multiples of 4.

Record: _____, _____, _____, _____, _____, _____

  1. Make rectangles to find six multiples of each number:

a) 3 ______b)7 ______

c) 5 ______d)6 ______

Part C: Find least common Multiples

For this part use the following grid:

For each multiple of 2, shade in the triangle in the upper left corner of the box. For each multiple of 3, use vertical lines to shade in the triangle in the upper right corner. Using different colors may be helpful.

  1. List the common multiples (those with both a solid and striped triangle) of 2 and 3 less than 100.

Which number is the least common multiple of 2 and 3?

  1. For all of the multiples of 4 use horizontal lines to shade in the triangle in the lower left corner of the box. Use dots (or a color) to shade in the lower right corner of the box for each multiple of 6.

List the common multiples of 4 and 6 less than 100:

What is the least common multiple of 4 and 6?

  1. Find the least common multiple for each pair of numbers.

a) 3 and 5 _____b)4 and 7 _____

c)9 and 6 _____d)2 and 8 _____

  1. Find the least common multiple for each group of numbers.

a)2,3, and 5 ______b)3, 6, and 8 ______

c)3, 4, and 7 ______d)2, 5, and 9 ______