Find a prime factor of $7999973$ without a calculator

How would you go about finding prime factors of a number like $7999973$? I have trivial knowledge about divisor-searching algorithms.

Answer

The thing to notice here is that 7,999,973 is close to 8,000,000. In fact it is $8000000 – 27$. Both of these are perfect cubes. Differences of cubes always factor: $$a^3 – b^3 = (a-b)(a^2+ab+b^2)$$

Here we have $a=200, b=3$, so $a-b= 197$ is a factor.

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