I had the same question when I found this, so here's some sample (python) code that would find the nearest divisor with no remainder.
Num = 636 # Numerator we are seeking to divide with no remainder
Den = 8 # Initial denominator
max_iters = 15 # caps the maximum loops
iters = 1 # initialize counter
Deni = Dend = Den # vars for searching increasing and decreasing denominators
while Num%Den != 0:
Deni +=1 # searching increased vals
if Dend > 0 : Dend -=1 # searching decreased vals, but check 0 condition
if Num%Dend ==0: # found a 0 remainder denominator
Den = Dend # assign found denominator
elif Num%Deni ==0: # found a 0 remainder denominator
Den = Deni # assign found denominator
elif iters >= max_iters: # check loop count
Not as clean as a built in function, but hopefully it helps the next person.