text: help...i can't figure out the answer to this math problem? ok... what is the remainder when 5^500 is divided by 2? the answer is 1. solution: 5^n is alway something like: 5*5*5*....*5 and can never be perfectly divisible by 2, since none of its prime factors is 2, so you know it´s not zero. therefor, there will always be a remainder. this remainder must be necessarily less that 2, because if it were greater than or equal to 2, then you could "fit in another 2" into the quotient. it can then only be 1.   as a rule, any number that cannot be perfectly divided by 2 yield a remainder of one. think about it this way, if you have a group of people and you wanna form several pairs, either you have a perfect match or you have 1 person left, if you had another person left, you´d pair them up.