How many positive integral factors (including 1 and itself) does 36 have?

To find the number of positive integral factors of 36, we first need to express 36 as a product of prime numbers.

36 = 2^2 * 3^2

The number of positive integral factors of a number is determined by adding 1 to the power of each prime factor in the prime factorization and then multiplying these results together.

For 36, the prime factorization is 2^2 * 3^2.

So, the number of positive integral factors is (2+1) * (2+1) = 3 * 3 = 9.

Therefore, 36 has 9 positive integral factors.