Question

The number 832n is a multiple of 6 ,where n is a digit.Find the value of n.​

Answer 1

Given:

• The number 832n is a multiple of 6
• And n is a digit.

To find:

• The value of n.

Solution:

832n is the multiple of 6

Therefore,it must be divisible by 2 and 3.

i)832n is divisible by 2

⇒n is an even digit.

⇒n=0,2,4,6,8

ii)832n is divisible by 3

⇒the sum of the digits is a multiple of 3

⇒8+3+2+n=0,3,6,9,15,etc

⇒13n=0,3,6,9,15

From (i),we have

⇒n=0,2,4,6,8

iii)⇒n+13=13,15,17,19,21

From (ii) and (iii),we have

⇒n+13=15 or 21

⇒n=2 or 8

Hence,the required values of n are 2 and 8.

Hope it's helpful!