Divisibility Test of 2

What is Divisibility?

When we divide any number(dividend) by any other number(divisor), whatever the quotient may come, if the remainder is 0, we say that the dividend was divisible by the divisor.

What is Divisibility by 2?

When we divide any number by 2, and the remainder comes out  to be 0, we say that the number is divisible by 2 and if the remainder is non 0, we say the number is not divisible by 2.

We can not always actually divide the number by 2 and then check whether the number is divisible or not, so we use the test of divisibility.

What is the test of divisibility? Why can’t we use a multiplication table?

We cannot always use the multiplication table to check whether  any number is a factor of , because number can be as big as in lakhs or crore, we barely remember multiplication tables, remembering things like 20th factor of 2, etc. would be impossible for humans, but one simple rule is divisibility test of 2 can easily tell us that whether the number is a factor of 2 or not, however large- millions, billions or trillions a number is.

What is the magical rule?

Just remember this simple rule, you will be able to solve and find whether number is factor of 2 or not within seconds-

Focus the unit’s digit of the given number. 

If the unit’s digit of the number is 0,2,4,6,or 8, you can confidently say that the number is divisible by 2.

This simple statement is applicable everywhere, on 2 digit, 3 digit, 4 digit etc, each natural number.

Special case of number 0: Even though some may argue that the number 0 also have 0 at unit’s place, then why can’t it be considered divisible by 2, as per what mathematician had said-

0 divided by any number is not defined in math.

How does this test of divisibility makes your calculations easy?

1. You can use it easily to check LCM(least common multiples) and HCF(highest common factor) :

Example: if you were to find LCM of 2 and 36, we can clearly see that 36 has 6 in unit place, and if divisible by 2, and is said to be a factor of 2, so simply their least common multiple will be 36 itself. 

If the number would not have been a factor of 2, we would have used other methods of finding LCM and it would have been a greater number.

2. While cancellation, dividing or cross multiplication :

When you are solving mathematics, it’s easier for students to cancel out the common factors quickly, so that the numbers come in their simplest forms, ratios and fractions.

So when we see, if both numbers are divisible by 2, we can simply divide both of them by 2 and make our calculations easier.

Example: If we see numbers like 150/32, we simply see common factor 2(as both are divisible by 2), we can simply divide both by 2 and get simple form 75/16.

Now few examples of questions on the topic: 

Q.1 Find whether number 102445 is divisible by 2 or not?

Ans.- The number 102445 has 5 at the unit place, so the number is not divisible by 2, because it does not pass the test of divisibility rule.

Q.2  Simplify: 154 divided by 16 (indirect usage in simplifying)

Ans.- We simply see that numbers 154 and 16 are both divisible by 2 and pass the test of divisibility, so we can simply divide both by 2, and simply it, so we get the answer- 77/8, and it cannot be simplified further because 77 is a prime number.

Q.3 Find the odd one out: ( 16, 18, 2256, 28934, 54333)

Ans.-  It will be extremely difficult for the student to find the logic in such a large and diverse set of numbers , but the divisible test will simply help you to find the odd one out, as number 54333 is not divisible by 2 and rest all numbers are, it is the odd one out. This is how a complex looking number is solved easily with this easy test of divisibility. 

Q.4 Are the given numbers divisible by 2 or not?

122, 1456, 34896.

Ans.- All the given numbers have the unit place digit from the test of divisibility rule-0,2,4,6 or 8, so all the numbers are divisible by 2.

Conclusion:

Hope this article gave a clear understanding of the concept of divisibility test of 3. This article also makes sure that all the concepts are backed by proper examples so that students might have a better understanding of the topic.