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

Last updated date: 19th Jul 2024
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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.

\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}
$\Rightarrow \text{Factors of 360 = }1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,70,90,120,180,360$
\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}
$\Rightarrow \text{Sum of factors = 1170}$