7/27/2019 CM2 Prime Time 4.1 the Product Puzzle

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I*lxmslis*tillltFact otizations s $earchin$for Bactor StringsSo*" numbers can be written as the product of several different pairsof factors. For example, 100 can be written as 1 x 700,2 x 50, 4 x 25,5 x 20,and 10 x 10.It is also possible to write 100 as the product of threefactors,such as 2 x 2 x 25 andz x 5 x 10.eeffiimg ffiem#p fmr Probfem@Can you flnd a longer string of factors with a product of 100?

Tlre Product PuzzleThe ProductPuzzle is a number-search puzzleinwhich you look for strings of factors with a productof 840. Two factor strings have been marked in thepuzzle at the right.How many factor stings can you find?

The Product Puzzle

lnvestigation 4 Factorizations: Searching for Factor Strings

7/27/2019 CM2 Prime Time 4.1 the Product Puzzle

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Problem @ finding Factor StringsIn the Product Plzzle,flnd as many factor strings for840 as you can. When you find a string, draw a linethrough it. Keep a list of the strings you find.It. What is the longest factor string you found?B. If possible, name a factor string with a productof 840 that is longer than any string you foundin the puzzle. Do not consider strings thatcontain 1.C. Choose a factor string with two factors. Howcan you use this string to find a factor stringwith three factors?D. How do you know when you have found thelongest possible string of factors for a number?E. How many distinct longest strings of factors arethere for 840? Strings are distinct if they aredifferent in some way other than the order inwhich the factors are listed.

A9E j Homework starts on page 5G.

q%l*incting rhe Longesr Factor SrringThe strings of factors of a number are called factorizations of that number.In Problem 4.1,you saw that the longest possible factor string for g40 ismade up of prime numbers. we call this string the prime factorization of840.In fact, the longest factor string for any whole number is the primefactorization. Can you explain why?

ffieee*aag ffiea$y for probrem@when you look for the prime factorization of a number, it helps to have alist of prime numbers handy. Look back at the table of flrst moves youmade for the Factor Game. Make a list of all prime numbers less than 30.

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