1 & 2 are the only non-zero remainders you can get from dividing a whole number by 3.
the max remainder you can have when dividing by a number is that number minus 1 So 4 can only have 1, 2 and 3 as remainders. 9 can only have 1-8 and so on.
2, 1 or 0.
10.
Any uneven integer can be represented in the form 2n+1. When you divide this number by 2, you will get n with 1 remaining (either +1 or -1)
It is 75.
Divide by the number repeatedly by two (until it is zero) and collect the remainders. For example: 13 / 2 = 6 Remainder 1 6 / 2 = 3 Remainder 0 3 / 2 = 1 Remainder 1 1 / 2 = 0 Remainder 1 Reading remainders from bottom yields: 1101
When 9 is used as a divisor, the remainders can range from 0 to 8. This is because the remainder is always less than the divisor. So, if you divide any number by 9, the possible remainders can be 0, 1, 2, 3, 4, 5, 6, 7, or 8.
When you divide by a divisor q, the remainders can only be integers that are smaller than q. If the remainder is 0 then the decimal is terminating. Otherwise, it can only take the values 1, 2, 3, ... ,(q-1). So, after at most q-1 different remainders you must have a remainder which has appeared before. That is where the long division algorithm loops back into an earlier pattern = repeating sequence.
When you divide by a divisor q, the remainders can only be integers that are smaller than q. If the remainder is 0 then the decimal is terminating. Otherwise, it can only take the values 1, 2, 3, ... ,(q-1). So, after at most q-1 different remainders you must have a remainder which has appeared before. That is where the long division algorithm loops back into an earlier pattern = repeating sequence.
In division by three, possible nonzero remainders are 1 and 2.
One way to divide the alphabet into five groups is by using the concept of modular arithmetic. With the English alphabet having 26 letters, we can assign each letter a numerical value (A=0, B=1, ..., Z=25). We then divide these numerical values by 5 and group the letters based on the remainder. Group 1 would consist of letters with remainders of 0, Group 2 with remainders of 1, and so on until Group 5 with remainders of 4. This method ensures an equal distribution of letters across the five groups.
1