If x, y, and z are integers, is x/(yz) an integer?

Here's how I approached it:

Solution required:

x/(yz) is an integer if both y and z are factors of x together, and not just individually

Information Given:

Option 1: y is a factor of x more than once

This implies x = c * y^a where c is some other constant product of the remaining factors of x and a is an integer > 1

BUT

we know nothing about z, so the option is NOT SUFFICIENT

Option 2: All of the prime factors of z are also factors of y.

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An important concept to know here:

Consider the number 36. On prime factorization we get:
36 = 2 * 2 * 3 * 3

When we say "ALL PRIME FACTORS" we mean not just the two unique prime factors (2 and 3) but also the repetitions of these unique prime factors.

So, all prime factors = 2,2,3,3

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With this in mind, z is a factor of y

However, we don't know the relationship of x with z or y, hence option 2 is NOT SUFFICIENT

Option 1 and 2 together

From 2, we know that z is a factor of y
From 1, we know that x = c * y^a where a is an integer >1

On combining 1 and 2, we know that yz is a factor of x, therefore x/(yz) is an integer.

Both together are SUFFICIENT.

Answer is C