DIVISIBILITY RULE FOR 4

Problem 1 :

Which of these numbers are divisible by 4?

a) 482   b) 2556  c) 8762  d) 12368  e) 213 186

Solution :

a) 482 

In the given number 482, the last two digits are not zeroes.

And also, the number formed by the last two digits is 82 which is not divisible by 4.

So, the given number 482 is not divisible by 4.

b) 2556 

In the given number 2556, the last two digits are not zeroes.

But, the number formed by the last two digits is 56 which is divisible by 4.

So, the given number 2556 is divisible by 4.

c) 8762 

In the given number 8762, the last two digits are not zeroes.

And also, the number formed by the last two digits is 62 which is not divisible by 4.

So, the given number 8762 is not divisible by 4.

d) 12368 

In the given number 12368, the last two digits are not zeroes.

But, the number formed by the last two digits is 68 which is divisible by 4.

So, the given number 12368 is divisible by 4.

e) 213 186

In the given number 213 186, the last two digits are not zeroes.

And also, the number formed by the last two digits is 86 which is not divisible by 4.

So, the given number 213 186 is not divisible by 4.

Problem 2 :

If the product of 4864 x 9P2 is divisible by 12, the value of P is 

a)  1     b)  5    c) 6      d) 8

Solution :

To check if the number is divisible by 12, it must be the multiple of 4 and 3.

In the given numbers, the first number 4864 is 

• not divisible by 3, because 4 + 8 + 6 + 4 ==> 22
• divisible by 4, because the last two digits 64 is divisible by 4.

To be 4864 x 9P2 divisible by 12, 9P2 must be divisible by 3.

9 + P + 2 ==> 11 + P

If p = 1, then we will get 12. It is divisible by 3.So, the required number is 1.

Problem 3 :

Consider the numbers of the form 3__8. Which digits could be put in place of ___.So that the number 3___8 is :

a) even  b) divisible by 3  c) divisible by 4 

Solution :

a) even 

The given number 3__8 is already a even number, because it ends with 8.

So, any number between 0, 1, 2, ...........9 can be filled in the place of ___.

b) divisible by 3

In a number, if the sum of all the digits is divisible by 3 or a multiple of 3, then the number is divisible by 3.

Let x be the unknown.

Add all the digits in the number 3x8.

3 + x + 8   = 11

x = 1

3 + 1 + 8 = 12

So, the number to be filled in the place of ___ is 1.

c) divisible by 4

In a number, if the last two digits are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

Let x be the unknown.

3x8

Put x = 2

328

Considering the last two digits, 28 is divisible by 4.

Problem 4 :

There are 360 minutes of monthly cell phone minutes for 4 people in a family. Can each person get the same number of minutes per month? If so, how many?

Solution :

Total number of minutes = 360

Number of people = 4

By dividing the total number of minutes by 4, we will get number of minutes each person gets.

= 360/4

= 90

So, each person will get 90 minutes per month.

Problem 5 :

Assume that there are 365 days in a year. Describe the possible number of days in a week so that there is an exact number of weeks in a year.

Solution :

Number of days in the week = 7

But in this way, we will not get equal number of days in each week. 365 ends by 5, so it must be divisible by 5.

= 365/5

= 73

So, the year consist of 73 weeks each week consist of 5 days.

Problem 6 :

A shopkeeper packs pencils in boxes of 6. He has 5784 pencils. Will he be able to pack them all without leaving any pencil ? Show how you decide.

Solution :

Total number of pencils = 5784

number of pencils = 6

When 5784 is divisible by 6, then we may understand that we will be able to pack them without leaving any pencil.

= 5784/6

= 964

5784 is exactly divisible by 6 will be able to pack with 964 boxes without leaving any pencil.

Problem 7 :

A teacher writes the number 145431 on the board and asks if it is divisible by 11. Help the class decide, showing each step clearly.

Solution :

The difference between the sum of alternative digits is 0 or multiples of 11, then it is divisible by 11.

1 + 5 + 3 = 9

4 + 4 + 1 = 9

= 9 - 9

= 0

Since the difference is 0, the given number 145431 is divisible by 11.