- **Number Theory**
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- - **Counting Problem**
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Counting ProblemHow many ways can 1,000,000 be expressed as a product of two natural numbers? (View 100*10,000 as different from 10,000*100.) As a product of three natural numbers? |

Re: Counting Problem1,000,000 = 2?5?, so any divisor must be of the form where x and y are in {0,1,2,3,4,5,6}. If it is a product of two numbers, the first determines the second, so you could write down the answer straight away. See if you can spot the pattern for three numbers (pick a number for the first and look at possibilities for the other two). |

Re: Counting ProblemI can see how to find the solution for the first part of this problem (49). I am still having trouble finding the solution to the second part of this problem. |

Re: Counting ProblemYou can re-express the first part of the problem additively: How many ways can you choose nonnegative a,b,c,d with a+b = 5 and c+d = 5? The second part, so expressed, is: How many ways can you choose nonnegative a,b,c,d,e,f with a+b+c = 5 and d+e+f = 5? In both cases you'll have to decide how to handle repetition. |

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