Divisibility by 4

Introduction

The division is an important part of mathematics, but it becomes difficult to solve for large numbers like 23900. However, in the number system, we have a solution to this problem in the form of divisibility rules, which can determine whether a number is particularly divisible by another number. To address this issue, we will check if a number is divisible by 4 rules and how to determine whether A number is defined as perfectly divisible by four or not. In addition, because divisibility is an important topic in quantitative aptitude, we will understand some of its questions. 

Divisibility by 4 

The divisibility rule of 4 is often studied under the number system and states that the number is divisible by 4 if the last two digits of the number are divisible by 4. It is generally denoted as divisibility by 4. The first four whole numbers divisible by 4 are 0,4,8,12 and 16. All these are the multiples of 4, and every multiple of 4 is exactly divisible by 4.

What is the divisibility rule of 4? 

A number is divisible by four if it fulfills two conditions:

• The final two digits of a whole number are zeros. This means that the number has 0 in the tens and ones places. A whole number’s last two digits from an amount that is precisely divisible by four.

Now, let’s understand the above conditions of divisibility by 4 by some examples: 

Find 712 and 814 are completely divisible by 4? 

To solve the problem, let’s get to the rule of divisibility by 4 rule that the last two digits of a number are divisible by 4. 

In the first number is 712, the last two digits constitute 12 which is divisible by 4; hence the number is completely divisible by 4 and will give 128 as an answer. 

And in the case of the second number, the last two digits are 14, which is not completely divisible by four and will give 2 as a reminder. 

Find if 1200 is divisible by 4? 

 As in ones and tens, there is 0 present, which means that 1200 is divisible by 4 and gives 300.

Divisibility Rule of 4 for Large Numbers

Just like another number, you need to check the last two digits of a number and if it is divisible by 4 or it is 0 then the number is completely divisible by 4.

For example, consider a number 36236, and in this, the last two digits 36 are divided by 4 then the number is divisible with 9059.

 List of numbers divisible by 4? 

Let’s discuss some of the lists of numbers divisible by 4. 

As there are 25 numbers in between 0 and 100 which are divisible by 4

4, 8, 12,16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.

And as 100 ends with 0, the pattern repeats itself in the next 100 numbers. 

104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200.

Now, there are 25 numbers above 100, and 0 is repeating in 200 as well. The same pattern will repeat in ahead numbers. 

The largest 4 digit number exactly divisible by 88 is? 

To solve this problem, we will use four rules of divisibility.

Find the most significant four-digit number and

As we all know, 9999 is the largest four-digit number.

And if we divide 9999 by 88. As a result, we get 55 as a remainder.

Now we need to subtract 55 from 99. i.e.

  9999-55 = 9944

Hence, The largest four-digit number that is divisible by 88 is 9944.

How many two-digit numbers are divisible by 4? 

To solve this problem, first, find the two-digit number divisible by 4.

The Numbers divisible by 4 are 12, 16, 20, … 96.

Now, this is an AP with a=12.

Common difference, d= 16-12 = 4

tn = a + (n-1) d       

96 = 12 + (n-1)4

84 = 4n – 4

88 = 4n

So n = 88/4 = 22

Here, (a= 1st term) 

          (d= common difference)                                            

          (n= number of terms)

Hence, there are 22 two-digit numbers divisible by 4.

Conclusion

As the divisibility rule is an essential part of mathematics, mastering it will help you with various quantitative problems. And in this article, we learned about divisibility by four rules and how to determine if a number can be perfectly divisible by 4. It can be a small or large number, but it will make one’s division process much easier. And as we discussed in the article, the divisibility rule allows you to excel in a variety of problems involving arithmetic progression and a list of numbers, and how you can create a list of numbers divisible by 4 and many others.