Find a quotient and a remainder without using division or modulo

divide.py

# Quotient and Remainder without using division

def divide (num, div):
    low, high = 0, num
    d = high - low
    
    # Keep going until there's no more midpoints between high and low
    # Need to find the value for x such that x*div ~ num
    while d > 1:
        # Calculate d here or there's one iteration too few
        d = high - low
        # Rshift kinda sorta halves the number
        # Enough to find a midpoint
        mid = low+(d>>1)
        
        # Is the midpoint*div higher than the num?
        # If so, x is between low and mid
        # Otherwise x is between mid and high
        if mid*div > num:
            high = mid
        else:
            low = mid
    return mid, num-mid*div

# Should print (3, 2)
# 3*3 == 9
# 11-9 = 2
print (divide (11,3))

Basically a search for a number in a dataset - but what are we searching for?
Looking for a number n such that n*div is very close to num. Find the n that produces a number the closest to num without exceeding it and that's your answer