If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

Solution:

We know that, according to divisibility rules, if the sum of the digits of a number is divisible by 3, then the given number is a multiple of 3.

• Since 31z5 is a multiple of 3, the sum of its digits will also be a multiple of 3.
• Sum of the digits of 31z5 is 3 + 1 + z + 5 = 9 + z is a multiple of 3.
• This is possible when 9 + z is any one of 0, 3, 6, 9, 12, 15, 18, and so on ...

For, 9 + z = 0 ⇒ z = 0 - 9 = -9. Not possible as x is a single digit positive number.

For, 9 + z = 3 ⇒ z = 3 - 9 = -6. Not possible as x is a single digit positive number.

For, 9 + z = 6 ⇒ z = 6 - 9 = -3. Not possible as x is a single digit positive number.

For, 9 + z = 9 ⇒ z = 9 - 9 = 0

For, 9 + z = 12 ⇒ z = 12 - 9 = 3

For, 9 + z = 15 ⇒ z = 15 - 9 = 6

For, 9 + z = 18 ⇒ z = 18 - 9 = 9

Since z is a single-digit number, the value of 9 + z can only be 9, 12, 15 or 18.

Thus, z can have any of the four values 0, 3, 6, or 9.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 16

Video Solution:

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

Class 8 Maths NCERT Solutions Chapter 16 Exercise 16.2 Question 4

Summary:

If 31z5 is a multiple of 3, where z is a digit, z can have any of the four values 0, 3, 6, or 9.

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