Question

Give the divisibility rule of 9 and 8 . If 31z5 is a multiple of 9, where z is a digit, what is the value of z?​

Answer 1

Answer:

Give the divisibility rule of 9 and 8 . If 31z5 is a multiple of 9, where z is a digit, what is the value of z?

Answer 2

Step-by-step explanation:

Given :-

31z5 is a multiple of 9, where z is a digit.

To find :-

what is the value of z?

Give the divisibility rules of 9 and 8 ?

Solution :-

Divisibility by 8:-

A number of more than three digits is divisible by 8, if the number formed by the last three digits (from units place ) is divisible by 8.

(or)

A number is divisible by 8 if the last three digits of a number are zeroes.

Divisibility by 9:-

If the sum of the digits of a number is divisible by 9 (multiple of 9) then the number is divisible by 9.

Given number = 31z5

It is a multiple of 9

=> It is divisible by 9

So, The sum of the digits is a multiple of 9

=> 3+1+z+5

=> 9+z

If 9+z is a multiple of 9 then

9+z must be equal to 9,18,27,...

The least number = 9

=> 9+z = 9

=> z = 9-9

=> z = 0

Therefore, z = 0

Answer:-

The least possible value of z for the given problem is 0

Check:-

If z = 0 then the given number becomes 3105

Sum of the digits = 3+1+0+5 = 9

So, 3105 is a multiple of 9.

Used formulae:-

Divisibility by 8:-

A number of more than three digits is divisible by 8, if the number formed by the last three digits (from units place ) is divisible by 8.

(or)

A number is divisible by 8 if the last three digits of a number are zeroes.

Divisibility by 9:-

If the sum of the digits of a number is divisible by 9 (multiple of 9) then the number is divisible by 9.