Problem 4.1 The Product Puzzle - Factor Strings Numbers can be written as the product of several pairs of factors. What are the factor pairs for 100? Can you write 100 as a product of three factors? How? Is it possible to final a longer string of factors with a product of 100? How? 2 x 2 x 25 4x5x5 5 x 2 x 10 Factors multiplied together to make a product are known as factor strings or factorizations of the number. In problem 4.1, you are going to be looking for factor strings for the number 840. How many factor strings can you find? Find as many as you can before completing questions A - E. There are many factor strings that you can find. Some are below. 5 x 42 x 4 56 x 3 x 5 420 x 2 70 x 12 120 x 7 280 x 3 84 x 10 105 x 8 28 x 6 x 4 21 x 2 x 4 x 5 Prime Time Problem 4.1 Answers A.) Answers will vary, but the longest string in the puzzle is: 2 x 2 x 2 x 3 x 5 x 7. B.) It is not possible to find a longer string than is in the puzzle. The longest possible string is 2 x 2 x 2 x 3 x 5 x 7. C.) Some strings can be broken down further to get longer strings. For example 420 x 2 can be split up into 210 x 2 x 2. D.) If all the numbers in a string are prime, the string is the longest possible. E.) Except for order, every whole number has exactly one longest string.