when the number is an even, as in 30's case, from the 1 to that EVEN, the number of even and odd integers are equal.

Bump for further discussion.

Regards

Prime factors of 30=2*3*5 whose total factors would be (1+1)(1+1)(1+1)=8????

How did you calculate the total factors -- What is this (1+1)(1+1)(1+1)=8????

shortcut
number of total factors in 30=2^1*3^1*5^1
=(1+1)(1+1)(1+1)
now to get odd and even factors
consider only 1st element in total factor formula e.g(2+1(1+3))
on this example even part is first 2(1+3) and odd factor =1(1+3)

now in our question we can apply the same for all.
even is =1(1+1)(1+1)=4



but be careful when you apply this. e.g. 125=5^3 now in this there is no even factor ,only odd factors.
also consider this for example, 75=5^2*3^1=no even factor

Good take.