Answer

Verified

347.1k+ views

**Hint:**In this type of question we have to use the concept of factorisation. We know that the factorisation of a number means to break it into numbers that can be multiplied to get the original number. In this example first we have to find all possible factors of the number 360 and then we have to add all of them to obtain the sum of all factors. To find the factors of the number 360, we have to find the divisors of 360 which does not leave any remainder.

**Complete step by step answer:**

Now, we have to find the sum of all the factors of the number 360.

So, let us find all possible factors of 360.

\[\begin{align}

& \Rightarrow 360=1\times 360 \\

& \Rightarrow 360=1\times 2\times 180 \\

& \Rightarrow 360=1\times 2\times 3\times 60 \\

& \Rightarrow 360=1\times 2\times 3\times 4\times 15 \\

& \Rightarrow 360=1\times 2\times 3\times 4\times 5\times 3 \\

\end{align}\]

Now, the factors of 360 are formed by taking these factors individually and then in groups. So that, the all possible factors of 360 are as follows:

\[\Rightarrow \text{Factors of 360 = }1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,70,90,120,180,360\]

And hence, the required sum of the factors of 360 is

\[\begin{align}

& \Rightarrow \text{Sum of factors = }1+2+3+4+5+6+8+9+10+12+15+18+20+24 \\

& \text{ }+30+36+40+45+60+70+90+120+180+360 \\

\end{align}\]

\[\Rightarrow \text{Sum of factors = 1170}\]

Hence, the sum of all the factors of the number 360 is 1170

**So, the correct answer is “Option d”.**

**Note:**In this type of question students have to take care in writing possible factors of 360. Students have to remember that for any number, 1 and that number itself that is 360 are also the factors of the number here it is 360. Students have to take care; do not forget to consider 1 as a factor of 360. Also students have to take care in the calculation part during addition of factors.

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