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Prime factorization of $600 = 2^3 \times 3 \times 5^2.$

Total no of divisors $= (3+1) (1+1) (2+1) = 4 \times 2 \times 3 = 24$ divisors

Here, we are choosing either $0, 1 , 2$ or $3, 2's$ so $3 + 1 = 4$ choices for $2$ and so on for all.

In case we do not choose any of the above factors, we get $1$ as divisor!
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600= 2*2*2*3*5*5=2^3*3^1*5^2

Hence no of divisors= (3+1)(1+1)(2+1)=24

Similarly the Lt Sin x/x as x tends to zero can be computed using L Hospital's rule where the initial form is (0/0). It come to 1.
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