Integer Division
An integer division (or division with remainder) is a way of dividing in which you only count the whole number of times that one number fits into another, without looking at the digits after the decimal point. In many cases, one number does not fit into another number exactly a whole number of times. The value that remains after an integer division is called a remainder. With the calculator below, you can easily calculate how many times a number fits into another number as a whole and what the possible remainder (R) is.
Integer division calculator
The integer division as part of the long division
In long division, you try to divide a large number by a smaller number step by step. Integer division plays a crucial role here, because you always want to know how many times the divisor fits into another number? This is exactly what integer division does: it gives you the whole number of times the divisor fits into it, without commas or decimals. For example:
The 5 fits 4 times into the 23, because:
(after all 5 × 5 = 25)
Determining the remainder
After finding the quotient (the whole number of times), you calculate the remainder. You do this by multiplying the quotient by the divisor and subtracting this from the number you are dividing (the dividend):
The remainder is important because you carry it over to the next step of long division (or if the remainder is 0, you're done).
In long division, you repeat this process over and over again: integer division determines how many times the divisor fits, and the remainder leads to the next step. Without this insight, you are more likely to make mistakes, for example by stopping too early or calculating incorrectly.
Understanding integer division in long division
Integer division is a method of dividing numbers where only whole number results are considered, and any leftover value is called the remainder. This concept is essential in long division, as it helps determine how many times the divisor fits into parts of the dividend without using decimals. By repeating this process—finding the quotient and remainder—long division solves complex division problems step by step. Use the integer division calculator above to help you perform long division by showing how many whole times one number fits into another and what the remainder is.
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