Question

find all the possible values of z for which 54z is divisible by 9 also find each such number​

Answer 1

Answer:

z = 0 or z = 9

And corresponding number are

540 and 549 respectively    

Step-by-step explanation:

Let   z = 0

Then

54z = 540

And since 54 is divisible by 9 hence 54×10 = 540 is also divisible by 9

Now let z = 1

Then

54z = 541 = 540 + 1

Since 540 is divisible by 9 but 1 is not divisible by 9 so

540 + 1 = 541 is not divisible by 9

Similarly letting z = 2 or 3 or 4 or 5 or 6 or 7 or 8

Because

54z = 540 + z              

When   0 < z < 9  Then

540 + z = 54z is not divisible by 9

AND

When z = 9  Then

54z = 549 = 540 + 9

Since 540 is divisible by 9 and 9 is also divisible by 9 so

540 + 9 = 549 is also divisible by 9

Thus

There are two possibilities of z which are 0 and 9

So

z = 0 or z = 9

And corresponding number are

540 and 549 respectively