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# Finding the Formula for the Maximum Product of Any given Number When Split into Parts

The objective of this coursework is to find the formula that gives the maximum product of any given number when split into parts For the first part of the coursework I am going to investigate the splitting of a number into two parts then three parts and four Parts For each number of parts This will result with a formula that gives the maximum product Pairs Starting number 12 PAIRS WHICH TOTAL 12 PRODUCT OF THE PAIR 120 0111 11102 2093 2784 32 75 35 66 3657 3548 3239 2710 20111 11 012 0 TEST FOR THE MAXI PRODUCT I will assume my maxi product is in the range between 75 and 57 because this where the product is at its highest So 69 513519 59 613599 Neither of these are higher than 36 So for my starting number 12 I have used the pairs 6 and 6 and my maxi product is 36 Starting number 10 PAIRS WHICH TOTAL 10 PRODUCT OF THE PAIRS 100 0 91 9 82 16 73 21 64 24 55 25 46 24 37 21 28 16 19 9 010 0 TEST FOR THE MAXI PRODUCT The maxi product lies between 64 and 46 because it these two numbers have the highest product 5 x 525 6 424 45 552475 Neither of the products are higher than 25 For my starting number 10 I have used the pair 55 and my maxi product is 25 Starting number 14 PAIRS WHICH TOTAL 14 PRODUCT OF THE PAIRS 1400 131 13 122 24 113 33 104 40 95 45 86 4877 49

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