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Find the sum of all the factors of the number 360
(a) 1205
(b) 624
(c) 525
(d) 1170

seo-qna
Last updated date: 19th Jul 2024
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Answer
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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.