Why does the remainder be less than the divisor

The answer is obviously 4, the remainder of 39 divided by 5. The quotient is 7, meaning each person got 7 oranges and there were 5 people, so a total of 35 oranges got divided amongst these 5 people. Well, imagine if 5 or more oranges remain, you can still go ahead and distribute one more orange to each person.

So it means 5 or any larger number cannot be the answer. Therefore, the remainder should be less than 5. In remainder problems, the question might trick you with a negative value of d. For example, what is the remainder when you divide an integer by -6? Remember -6 gives us the absolute value or the magnitude of -6, which is 6. What is the minimum possible remainder when an integer is divided by 11?

Since, 0? In other words, n is completely divided by d. What is the minimum possible remainder when an integer is divided by? Again, the minimum possible value of the remainder is 0.

And what is the maximum possible remainder when an integer is divided by 11? And what is the maximum possible remainder when an integer is divided by? For a negative d , 0? If d is positive, the maximum possible value of the remainder is 1 less than d. If d is negative, the maximum possible value of the remainder is 1 less than d.

Like most people who take the GRE, your Math knowledge might be a little rusty. Wiki User. The remainder is less than the divisor because if the remainder was greater than the divisor, you have the wrong quotient. In other words, you should increase your quotient until your remainder is less than your divisor! The remainder must be less than the divisor, otherwise you are not doing the division correctly.

Because if the remainder is greater, then you could "fit" another divisor value into it. Thus, the remainder is always lower than the divisor. If the remained was bigger than the divisor than the divisor could still be taken out of the remainder. A remainder can be any non-negative number that is less than the divisor.

If the remainder is bigger than the divisor, the divisor can go into it another one or more times until the remainder is brought into that range. The remainder has to be less than the divisor. Otherwise your answer is wrong.

One less than the divisor. It is always one less than the divisor. If you divide correctly, the remainder will always be less than the divisor.

It must be less else you have not divided properly; you could divide again 1 or more times! If the remainder is equal to the divisor or equal to a multiple of the divisor then you could divide again exactly without remainder.

If the remainder is greater but not a multiple of the divisor you could divide again resulting in another remainder. This is 4 remainder 1. Let's say our answer was 3 remainder 3; as our remainder "3" is greater than the divisor "2" we can divide again so we have not carried out our original division correctly!

To determine the remainder, you would take 63 and see how many times your divisor fits into it. That will give you a number, which when multiplied by the divisor will be less than 63, and smaller than the divisor. Subtract the result of your divisors times your quotient from 63, and that number is the remainder. If the remainder is greater than the divisor then you can divide it once more and get one more whole number and then have less remainders.

Because if the remainder was larger than the divisor, then the divisor could go into the dividend again. Because if the remainder is bigger than the divisor, the quotient can be increased and that will reduce the remainder.

You can keep doing as long as the remainder is larger than the divisor. You stop only when it becomes smaller. If the remainder were greater than the divisor, you'd be able to take another divisor out of it.

No it shouldn't because the divisor should always be bigger. Any number less than eight. The answer depends on the divisor - which must me greater than 3.

You want to share the cookies equally among your friends and yourself. You will be distributing them in the following way. Here, you can see that there are 3 cookies "remaining" after the distribution. These 3 cookies cannot be further shared equally among the 4 of you.

Hence, 3 is called the "remainder". Also, on observation, the remaining 3 cookies are less in number than the 4 people, with whom the cookies have been shared.

We can understand that the remainder is always lesser than the divisor. Remainder is a part of a division. It is a left-over digit we get while performing division.

When there is an incomplete division after certain steps we get remainder as a result. The remainder is left over when a few things are divided into groups with an equal number of things. Let's recall the scenario we discussed earlier 15 cookies being shared equally among 4 children. In other words, 15 cookies had to be divided into 4 equal groups.

We were left with 3 cookies and hence, 3 were the remainder. Let us consider another example. Let us assume that 8 slices of pizza are to be shared equally among 2 children. How many pieces of pizza remain unshared? You can look at the picture below to understand how we have divided the slices of pizza equally between the two children. Thus, the remainder is 0 as no pieces of pizza are left unshared. We cannot always pictorially show how we divide the number of things equally among the groups in order to find the remainder.

Instead, we can find the remainder using the long division method. For example, the remainder in the above example on cookies can be found using long division as follows:. Thus, the remainder is 3. A remainder can also be a 0. The remainder on dividing 10 by 2, 18 by 3, or 35 by 7, is equal to 0. Here are some other examples of remainders.

Let us divide 7 by 2 using long division and see what the quotient and the remainder are. The quotient, divisor, the remainder can be together written as a mixed fraction to represent the dividend. The remainder forms the numerator of the mixed fraction, the divisor forms the denominator, and the quotient form the whole number part of the mixed fraction.

Given below is the list of topics that are closely connected to the remainder. These topics will also help you in solving problems related to the remainder. Example 1: What is the remainder when is divided by 23? Check if the answer you got is correct. Therefore, the remainder is Since we have the same values on both sides, our answer is correct.

Example 2: The number of days in the year was as it was a leap year. If 1 st Jan was a Monday, what day was it on 1 st Jan ? It is given that 1 st Jan was a Monday.