Question

find the value of z for which the number 471z8 is divisible by 9​

Answer 1

A number is exactly divisible by 9 if and only if the sum of its digits is exactly divisible by 9.

The sum of digits of the number 471z8 is,

$\displaystyle\longrightarrow\sf{s=4+7+1+z+8}$

$\displaystyle\longrightarrow\sf{s=z+20}$

Here z is a non - negative one digit number. And s should be exactly divisible by 9.

There's only one possible value for s.

$\displaystyle\longrightarrow\sf{s=27}$

$\displaystyle\Longrightarrow\sf{z=27-20}$

$\displaystyle\longrightarrow\sf{\underline {\underline {z=7}}}$

Hence 7 is the answer, and our number is 47178.

• 47178 = 9 × 5242