Europium
Europium has an atomic number of 63, which means it belongs to group number 63 in the periodic table.

Americium
Americium has an atomic number of 95, which means it belongs to the 95th period in the periodic table.

Gadolinium
Gadolinium has an atomic number of 64, which means it belongs to the 64th group in the periodic table.

Calculating x, y, and z
Based on the information given, we can determine the values of x, y, and z.

- x represents the group number of Europium, which is 63.
- y represents the period number of Americium, which is 95.
- z represents the most stable oxidation state shown by Gadolinium, which is not explicitly given.

Since the question does not provide the specific oxidation state of Gadolinium, we cannot determine the exact value of z. However, we can provide some information about the possible oxidation states of Gadolinium.

Oxidation States of Gadolinium
Gadolinium, being a lanthanide element, typically exhibits an oxidation state of +3. This is because the outermost shell of Gadolinium contains 7 electrons, and it tends to lose all 3 electrons to achieve a stable configuration.

In addition to the +3 oxidation state, Gadolinium can also exhibit other oxidation states, although they are less common. These include +2 and +4.

Therefore, the value of z, representing the most stable oxidation state shown by Gadolinium, can be assumed to be +3.

Final Answer
Based on the information provided, the value of x is 63 (group number of Europium), the value of y is 95 (period number of Americium), and the value of z is assumed to be +3 (most stable oxidation state shown by Gadolinium).