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Advanced Numerical Factoring

The content delves into advanced techniques for finding the prime factorization of numbers, particularly through the use of the difference of two squares formula, demonstrating its utility in simplifying complex numerical problems on the GRE exam.
  • Prime factorization is crucial for understanding the number of factors a number has and for simplifying complex numerical problems.
  • The difference of two squares is a powerful tool for factoring numbers that are difficult to factor through conventional means.
  • This technique is not only applicable to large numbers but also to decimals, offering an elegant solution to otherwise challenging problems.
  • Practical examples are provided to illustrate how to apply the difference of two squares formula to find prime factorizations and simplify decimals.
  • Practice problems are included to reinforce the understanding and application of the difference of two squares in various contexts.
Introduction to Prime Factorization
Applying Difference of Two Squares
Elegant Solutions for Complex Numbers
Decimals and Difference of Squares

Q: For the practice problem around 5:03, how does Mike come up with (1-000049)/(1-0.007) as a substitute for 0.999951/0.993? What's the best way to rewrite a number as "1 minus something?"

A: To be honest, he probably just used a calculator. :)

I know we discourage using the calculator too much, but there is definitely a time and place where it's appropriate to use. This is one of those cases! Any time you see a number with lots and lots of decimals -- and no easy way to convert it to a fraction -- then the calculator should be your go-to option!

So, to get the 1 minus a number, you just subtract the original numbers from 1, like so:

1-0.999951 = 0.000049

So, 0.999951 = 1 -0.000049