For each problem, write a complete descriptionof how you approached finding the

Question

For each problem, write a complete descriptionof how you approached finding the solution, including things thatyou tried that were not successful.  Identify the strategythat worked for you. Write any other comments orinclude picture/diagrams that you used.

1.      Three blocks of cheese weigh 650 kilograms, 680 kilograms,and 740 kilograms.  For the purpose ofpacking and to avoid waste, the cheese is to be cut into pieces ofequal weight.  How much should eachpiece weigh if the total number of pieces is to be as small aspossible?

Explanation / Answer

the measurement should be the greatest common divisorof the weights 650 , 680 , 740 kgs respectively. i.e. using the prime factorization method , 650 = 2* 325 = 2*5* 65 = 2* 5* 5*13                                                          680 = 2* 340 = 2* 2* 170 = 2* 2* 2* 85 = 2* 2* 2* 5* 17                                                           740 = 2* 370 = 2* 2* 185 = 2* 2* 5* 31 so, the greatest common divisor of the given weights = 2* 5 =10 so, the packing should be in the measures of 10 kg each to seethe available quantities in the same packings.

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