Find the remainder when (21)^80 divided by 22.

Confused by long division? By the end of this article you'll be able to divide 80 by 22 using long division and be able to apply the same technique to any other long division problem you have! Let's take a look.

Want to quickly learn or show students how to solve 80 divided by 22 using long division? Play this very quick and fun video now!

Okay so the first thing we need to do is clarify the terms so that you know what each part of the division is:

• The first number, 80, is called the dividend.
• The second number, 22 is called the divisor.

What we'll do here is break down each step of the long division process for 80 divided by 22 and explain each of them so you understand exactly what is going on.

80 divided by 22 step-by-step guide

Step 1

The first step is to set up our division problem with the divisor on the left side and the dividend on the right side, like we have it below:

We can work out that the divisor (22) goes into the first digit of the dividend (8), 0 time(s). Now we know that, we can put 0 at the top:

If we multiply the divisor by the result in the previous step (22 x 0 = 0), we can now add that answer below the dividend:

Next, we will subtract the result from the previous step from the second digit of the dividend (8 - 0 = 8) and write that answer below:

Move the second digit of the dividend (0) down like so:

The divisor (22) goes into the bottom number (80), 3 time(s), so we can put 3 on top:

If we multiply the divisor by the result in the previous step (22 x 3 = 66), we can now add that answer below the dividend:

Next, we will subtract the result from the previous step from the third digit of the dividend (80 - 66 = 14) and write that answer below:

So, what is the answer to 80 divided by 22?

If you made it this far into the tutorial, well done! There are no more digits to move down from the dividend, which means we have completed the long division problem.

Your answer is the top number, and any remainder will be the bottom number. So, for 80 divided by 22, the final solution is:

3

Remainder 14

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Extra calculations for you

Now you've learned the long division approach to 80 divided by 22, here are a few other ways you might do the calculation:

• Using a calculator, if you typed in 80 divided by 22, you'd get 3.6364.
• You could also express 80/22 as a mixed fraction: 3 14/22
• If you look at the mixed fraction 3 14/22, you'll see that the numerator is the same as the remainder (14), the denominator is our original divisor (22), and the whole number is our final answer (3).

Long Division Calculator

Next Long Division Problem

Eager for more long division but can't be bothered to type two numbers into the calculator above? No worries. Here's the next problem for you to solve:

What is 80 divided by 23 using long division?

Random Long Division Problems

If you made it this far down the page then you must REALLY love long division problems, huh? Below are a bunch of randomly generated calculations for your long dividing pleasure:

How to calculate 80 divided by 21

80 = dividend

3

3.8095

3 17/21

This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.

When you perform division, you can typically write down this operation in the following way:

where:

• a — Initial number you want to divide, called the dividend;
• n — Number you divide by; it is called the divisor;
• q — Result of division rounded down to the nearest integer; it is called the quotient; and
• r — Remainder of this mathematical operation.

When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise, the result will be correct in the terms of formulas, but will not make mathematical sense.

Make sure to check our modulo calculator for a practical application of the calculator with remainders.

🔎 If the remainder is zero, then we say that a is divisible by n. To learn more about this concept, check out Omni's divisibility test calculator.

1. Begin with writing down your problem. For example, you want to divide 346 by 7.
2. Decide on which of the numbers is the dividend, and which is the divisor. The dividend is the number that the operation is performed on – in this case, 346. The divisor is the number that actually "does the work" – in this case, 7.
3. Perform the division – you can use any calculator you want. You will get a result that most probably is not an integer – in this example, 49.4285714.
4. Round this number down. In our example, you will get 49.
5. Multiply the number you obtained in the previous step by the divisor. In our case, 49 * 7 = 343.
6. Subtract the number from the previous step from your dividend to get the remainder: 346 - 343 = 3.
7. You can always use our calculator with remainders instead and save yourself some time 😀

1. Make sure you have an unknown equal to two or more different modulos, e.g., x = d mod a, e mod b & f mod c.
2. Check that all modulos have the same greatest common divisor.
3. Multiply each modulo by all but one other modulo, until all combinations are found. For the above moduli, this would be: b*c, a*c, a*b.
4. Divide each number by the modulo that it is missing. If it equals the remainder for that modulo, e.g., (b*c)/a = d, leave the number as is.
5. If the remainder is not that for the modulo, use trial and error to find a positive integer to multiply the number by so that step 4 becomes true.
6. Add all numbers together once step 4 is true for all combinations.

It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.

Learning how to calculate the remainder has many real-world uses and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?

1. Set up your division, adding a decimal place followed by a zero after the dividend’s one’s column (if your dividend is already a decimal, add an additional zero to the end).
2. Perform the division as usual until you are left with the remainder.
3. Instead of writing the remainder after the quotient, move the remainder above the additional zero you placed.
4. If there is a remainder from this division, add another zero to the dividend and add the remainder to that.
5. Continue in this fashion until there is either: no remainder, the digit or digits repeat themselves endlessly, or you reach the desired degree of accuracy (3 decimal places is usually okay).
6. The result after the decimal place is the remainder as a decimal.

The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn’t entirely go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient, and 1 is the remainder.

Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!

There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.

The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case, it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.

The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

1. Subtract 7 from 24 repeatedly until the result is less than 7.
2. 24 minus 3 times 7 is 3.
3. The number that is left, 3, is the remainder.
4. This can be expressed as 3/7 in fractional form, or as 0.42857 in decimal form.