300
-2
1ExplanationNote the following:31=332=933=2734=8135=24336=72937=218738=6561You will see that the units digit of the powers of three cycles through the following: 3, 9, 7, 1. 3 raised to a multiple of 4 has 1 as the units digit. Because 2008 is a multiple of 4, 32008 has 1 in the units digit (and is thus the remainder when that number is divided by 5).
31 divided by 3 is 10 with remainder 1
33 divided by 7 is 4 with remainder 5
40*24 = 960 and 960/40 = 24
17
100
111
121
Probably many answers, but for example 100 / 8 = 96 remainder 4
-2
That's not possible. The largest single-digit number by which you might divide is 9. And, by definition, the remainder is always LESS than the number by which you divide. Thus, the largest remainder you can get, when you divide by 9, is 8.
The three-digit number that can be divided by every number less than 9 without a remainder is 504. This is because 504 is the least common multiple (LCM) of the numbers 1 through 8, which are 1, 2, 3, 4, 5, 6, 7, and 8. It meets the criteria of being a three-digit number and is divisible by each of these integers.
A dividend is is a number to be divided and a divisor is a number to be divided into a dividend. Here the dividend is a three digit number and is divided by a one digit divisor. The quotient or result is a two digit number as stated. So in math terms, we can state that the dividend is a three digit number and that the divisor is a one digit number.
To find the least three-digit dividend that gives a remainder of 4 when divided by 40, we can start with the smallest three-digit number, which is 100. We want to find a number ( x ) such that ( x \equiv 4 \mod 40 ). The smallest three-digit number that meets this condition is 104, because ( 104 - 4 = 100 ) is divisible by 40. Thus, the least three-digit dividend is 104.
-10
One possibility is 138.