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Exploring Factor Strings: The Product Puzzle of 840

Dive into the fascinating world of factorization with "The Product Puzzle," where you'll uncover various strings of factors that multiply to 840. This interactive number-search challenge allows you to discover and draw connections between different factor pairs. For instance, while you can identify pairs like 2 x 420, you can also find nested factors within these pairs, such as 21 x 2 x 4 x 5. The goal is to find as many unique factor strings as possible. Join the adventure and enhance your number sense!

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Exploring Factor Strings: The Product Puzzle of 840

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  1. 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. 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

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