Number Theory

Prime Factorization and Divisors

Prime Factorization and Divisors: Level 1 Challenges


50!51\Huge \frac{\color{#3D99F6}{50!}}{\color{#D61F06}{51}}

What is the remainder of the division above?

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

How many perfect squares are there between 101101 and 99999999?

Find the sum of the digits of 22999×53002\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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