Write an even square number smaller than 100.

I believe you mean what square number that is less than 100 has the most factors.

The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.

1 obviously only factors to 1*1.

4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1*n or p*p. example: 1*4, 2*2. We can eliminate those.

16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1*n, (p^3) * p, or (p^2*p^2). Example: 1*16, 8*2, or 4*4.

But 36 is 2*2*3*3 as it's prime factoring. This allows us to find more combinations of factors: 1*36, 2*18, 4*9, 12*3, or 6*6.