Question

If 31Z5 is multiple of 9 .where Z is a single digit number ,what is the value of Z.

Answer 1

Answer:

9

Z = 9

Step-by-step explanation:

We know that, a number is divisible by 9 only if the sum of digits of the number is divisible by 9.

And also it is given that the value of Z is a single digit number.

Thus replacing Z with 9 , we get,

31Z5 = 3195

Now checking its divisibility by 9,

3+1+Z+5 = 3+1+9+5 = 18

We already know that 18 is divisible by 9 . And also sum of 3+1+5 = 9. Thus value of Z will be surely equal to 9.

Answer 2

Answer:

Divisibility rule for 9 : The prime factors of 9 are 3 and 3. So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9. If it is, then the actual number is also divisible by 9.

Digit : 31Z5

So, we can find the value of Z by add them...

=> 3 + 1 + Z + 5 = 9 + z

We see that 9 is itself a multiple of 9, so we can add 9 to it, so it can again become the multiple of 9.

9 + Z = multiple of 9

9 + 9 = 18

18, which is multiple of 9.

Here, we cannot take any other multiple of 9.... ..like 18, 27 etc...

Bcoz, in the question, it is given that the value of z is single digit.... THAT'S WHY, thr value of z is 9.

Hence, the value of Z is 9.

HOPE IT HELPS ❤️