Question

If 63y54 is a multiple of 6, where y is a digit, find the value of y?

Answer 1

Answer:

we know that the divisibility rule of six is that if the number divided by two and three the that number will be divisible by six

so y= 0

Answer 2

We know for a number to be divisible by 6 , it must be divisible by 2 and 3 .

• For a number to be divisible by 2 it must have 0,2,4,6,8 as its ones digit .

• For a number to be divisible by 3 , the sum of all digits of that number must be a multiple of 3 .

so , in the case of 63y54 which is already a multiple of 2 as it has 4 in its unit's place , sum must be a multiple of 3 (for it to be multiple of 6)

=> 6 + 3 + y + 5 + 4 => 18 + y

now ,

we have , 18 + y as a multiple of 3 .

=> Therefore , y can have following values ,

y = 0

y = 3

y = 6

y = 9