Question

Write cardinal number of the following: {x: x is the factor of 3600 }

Answer 1

$$\begin{gathered} LetS=\left\{x:xisafactorof3600\right\} \\ 3600=36\times 100={\left(2\times 3\right)}^2\times {\left(2\times 5\right)}^2=2^2\times 3^2\times 2^2\times 5^2=2^4{3}^2{5}^2 \\ Result \\ IfanumberN=2^a{3}^b{5}^c{7}^d...thennumberoffactors=\left(a+1\right)\left(b+1\right)\left(c+1\right)... \\ Numberoffactorsof3600=\left(4+1\right)\left(2+1\right)\left(2+1\right)=5\times 3\times 3=45 \\ n\left(S\right)=45 \end{gathered}$$