Number Theory

# Prime Factorization and Divisors: Level 1 Challenges

$\Huge \frac{\color{blue}{50!}}{\color{red}{51}}$

What is the remainder of the division above?

Let $$Y = n(n+1)$$ for some positive integer $$n$$. Which of the following statements is true?

How many perfect squares are there between $$101$$ and $$9999$$?

Find the sum of the digits of $$\large 2^{2999} × 5^{3002}$$ when multiplied out.

Find the smallest positive integer which is both a perfect square and a perfect cube.

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