Maybe something like this:

A1: (a number.....eg 60)
C2: (lower limit.......eg 20)
D2: (lower limit.......eg 25)

This ARRAY FORMULA, committed with CTRL+SHIFT+ENTER
(instead of just ENTER), returns the first integer quotient:

B1: =INDEX(A1/ROW(INDEX($A:$A,C2):INDEX($A:$A,D2)),
MATCH(1,--(MOD(A1/ROW(INDEX($A:$A,C2):INDEX($A:$A,D2)),1)=0),0))

In the above example, the formula divides 60 by 20, 21, 22, 23, 24 and 25
and returns the first quotient that is a whole number: 3

Is that something you can work with?