Question

how many positive factors of 540 are there

Answer 1

540 contains 16 even and 8 odd positive factors

Answer 2

40=2^2 + 3^3 + 5^1

the number of all factors (divisors) for 540, 2+1=3, 3+1=4, 1+1=2 => 3*4*2=24 factors (divisors)

note that there 2^2 primes, 2 is even => a number is even if it is divided by 2 => number of the evens is 2 times more

e.g. for 1 odd there are 2 evens

24 factors=16 even+8 odd

you can test this with many numbers

say 12

/2 => 6
/2 => 3
/3 => 1

2^2 + 3^1 => (2+1)*(1+1)=6 factors => 2 evens for 1 odd

4 evens {2,4,6,12} and 2 odds {3,1}

..............

number 270 has 16 factors <=> 2^1 + 3^3 + 5^1 => 2*4*2=16