# If 56x32y is divisible by 18, find the least value of y.

**Solution:**

If 56x32y is divisible by 18 it means that it is divisible by 9 and 2, because 18 = 9 × 2

The __number__ is divisible by 2 if y is __even__.

A number is divisible by 9 if the __sum__ of its digits is divisible by 9.

Therefore,

5 + 6 + x + 3 + 2 + y = 16 + x + y

For 16 + x + y to be divisible x + y has to be at least 2.

Therefore x and y can assume values:

(a) x = 2, y = 0

(b) x = 1, y = 1 but y = 1 therefore it is not even and not divisible by 2

(c) x = 0; y = 2

From the above three values of x and y the least value of y = 0.

**✦ Try This:** If 45x21y is divisible by 12, find the least value of x + y.

If a number is divisible by 12 then the number is also divisible by 3 and 4 because 12 = 4 × 3

For the number to be divisible by 4 the number formed last two digits 1y has to be divisible by 4. The least number divisible by 4 is 12 which implies y = 2. (1)

For the number to be divisible by 3 the sum of its digits should be divisible by 3. Therefore 4 + 5 + x + 2 + 1 + y = 12 + x + y has to be divisible by 3. The least number divisible by 3 will be:

12 + x + y = 12 + 0 + 0 = 12

But if y = 0 then 10 will be last two digits and that will not be divisible by 4.

If y = 2

Then the least value x + y will be 6.

Since y = 2, x = 4

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 16

**NCERT Exemplar Class 8 Maths Chapter 13 Problem 74**

## If 56x32y is divisible by 18, find the least value of y.

**Summary:**

If 56x32y is divisible by 18, the least value of y = 0.

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