1. The Product Puzzle: Learning to Factorize 840
Prime Time Lesson 4.1
The Product Puzzle:
Learning to Factorize 840

2. Searching for Factor Strings
Some numbers can be written as the product of several different pairs of factors. For example, 100 can be written as:
1 x 100, 2 x 50, 4 x 25
when using only factor pairs.
Sometimes we can find other factors within our factor pairs. For example, 100 can also be written as:
2 x 2 x 25, 2 x 5 x 10 and 2 x 5 x 2 x 5!

3. The Product Puzzle
The Product Puzzle is a number-search puzzle in which you look for strings of factors with a product of 840.
This is an example of The Product Puzzle.

4. How many factor strings can you find?
Product Puzzle Goal
How many factor strings can you find?
The goal of the product puzzle is to find as many factor strings of 840 as you can.
For example, I know that 2 x 420 is a factor pair of 840. I will then use my pencil to draw a line through the numbers 2 and 420.

5. Product Puzzle
As I continue working on my puzzle, I think to myself, “what other factors can be created?”
I know that 42 X 20 is also a factor pair of 840. By crossing out these factors, I then know that I can also cross out 21 x 2 x 4 x 5 because I know that 21 x 2 are factors of 42 and 4 x 5 are factors of 20!

6. Product Puzzle
Continue to play crossing out as many factors as you can that make 840!

7. Product Puzzle