Why does 2 mod 4 = 2?

When you divide 2 by 4, you get 0 with 2 left over or remaining. Modulo is just the remainder after dividing the number.

To answer a modulo x % y, you ask two questions:

A- How many times y goes in x without remainder ? For 2%4 that's 0.

B- How much do you need to add to get from that back to x ? To get from 0 back to 2 you'll need 2-0, i.e. 2.

These can be summed up in one question like so: How much will you need to add to the integer-ish result of the division of x by y, to get back at x?

By integer-ish it is meant only whole numbers and not fractions whatsoever are of interest.

A fractional division remainder (e.g. .283849) is not of interest in modulo because modulo only deals with integer numbers.

This could be a good time to mention the modr() function. It returns both the whole and the remainder parts of a division.

print("\n 17 // 3 =",17//3," # Does the same thing as int(17/3)")
print(" 17 %  3 =",17%3," # Modulo division gives the remainder.")
whole, remain = divmod(17,3)
print(" divmod(17,3) returns ->",divmod(17,3),end="")
print(" because 3 goes into 17,",whole,"times with a remainder of",remain,end=".\n\n")

The way I go about it is, 2%4 can be interpreted as what is the highest factor of 4 that is less or equal to 2, and that is 0, therefore 2 (the left operand from 2%4) minus(-) 0 is 2