Final answer:
The value of z must be a multiple of 7, like 7, 14, 21, 28, etc., so that 7 is the greatest common factor of 35 and z.
Step-by-step explanation:
The value of z in the question can be determined using the definition of the greatest common factor (GCF). Since the GCF of 35 and z is 7, this means that both 35 and z have 7 as their highest factor in common. Given that 35 is already a multiple of 7 (35=5*7), z must also be a multiple of 7 to have a GCF of 7. Hence, z could be any multiple of 7, such as 7, 14, 21, 28, and so on, where z/7 is an integer.