Answer

Verified

308.1k+ views

**Hint:**In order to solve this question, we will go through by applying the divisibility rule of \[45\] to check which number is completely divisible by \[45\] . And we know that if the number is divisible by \[5\] and \[9\] then the number is divisible by \[45\] . So here we will use the divisibility test of \[5\] and \[9\] and check each option. Then we will conclude which option satisfies the divisibility test of both \[5\] and \[9\] . And hence we will get our required result.

**Complete step by step answer:**

Here in the question, we have to find the number which is divisible by \[45\]. So, first of all let’s understand the divisible rule of \[45\] i.e., divisibility rule of \[45\] is the number divisible by both \[5\] and \[9\]. Now we know that the divisibility rule of \[5\] is if the number ends with \[0\] or \[5\] then it is divisible by \[5\]. And the divisibility rule of \[9\] is if we add up all the digits and the addition is divisible by \[9\] then the number itself is also divisible by \[9\]

Now by using the above definitions we will check each option.

Option (a) is \[1,81,560\]

First let’s check the divisibility rule of \[5\].

Here, the last digit is \[0\] which means it is divisible by \[5\].

Now let’s check the divisibility rule of \[9\].

The sum of the digits is \[1 + 8 + 1 + 5 + 6 + 0 = 21\] and we know \[21\] is not divisible by \[9\].

Since, the number is only divisible by \[5\] and not \[9\].

Hence, the given number is not divisible by \[45\].

Now option (b) is \[3,31,145\]

So first let’s check the divisibility rule of \[5\].

Here, the last digit is \[5\] which means it is divisible by \[5\].

Now let’s check the divisibility rule of \[9\]. The sum of the digits is \[3 + 3 + 1 + 1 + 4 + 5 = 17\] and we know \[17\] is not divisible by \[9\].

Since, the number is only divisible by \[5\] and not \[9\].

Hence, the given number is not divisible by \[45\].

Now option (c) is \[2,02,860\]

So first let’s check the divisibility rule of \[5\].

Here, the last digit is \[0\] which means it is divisible by \[5\].

Now let’s check the divisibility rule of \[9\].

The sum of the digits is \[2 + 0 + 2 + 8 + 6 + 0 = 18\] and we know \[18\] is divisible by \[9\].

Since, the number is divisible by both \[5\] and \[9\].

Hence, the given number is divisible by \[45\].

Now let’s check the option (d) as well

Given number is \[20,38,550\].

So first let’s check the divisibility rule of \[5\].

Here, the last digit is \[0\] which means it is divisible by \[5\].

Now let’s check the divisibility rule of \[9\].

The sum of the digits is \[2 + 0 + 3 + 8 + 5 + 5 + 0 = 23\] and we know \[23\] is not divisible by \[9\].

Since, the number is divisible by only \[5\] and not \[9\].

Hence, the given number is not divisible by \[45\].

Therefore, from the above calculation we conclude that the number \[2,02,860\] is divisible by \[45\].

**Hence, option C is the correct answer.**

**Note:**Whenever we face such types of problems, the key concept for solving the question is to go through the divisibility rule of that number. Also remember that co-primes of any number can be used to check the divisibility of very large numbers. Also, the easiest way to verify the result is direct division of dividend through divisor. And if the remainder comes out to be zero, then it can be said that the dividend is completely divisible by the divisor.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE