Long Division
2026-02-21 20:26 Diff
https://brightchamps.com/en-us/math/numbers/long-division

Now let’s learn how to do the long division method, follow these steps to perform the long division method. 

Step 1: Check if the first digit (or first group of digits) of the dividend is greater than or equal to the divisor. 
 

For example, dividing 27 by 2. Here, the dividend (27) is greater than the divisor (2). 

Step 2: Now find a multiple of the divisor which is less than or equal to the dividend. Make sure the quotient is less than 9 in this step.

Here, 2 × 1 = 2, the first digit in the quotient is 2. 

Step 3: Find the difference between the multiple of the divisor and the first digit of the dividend. Here the difference is 0 as 2 − 2 = 0. 27 / 2 = 13.5

Step 4: Bring down the next digit (7), forming 07. Divide 7 ÷ 2 = 3; remainder is 1 (since 2 × 3 = 6, 7 – 6 = 1). The quotient digit is 3.

Step 5: Repeat steps 2 to 4 until the remainder is zero or less than the divisor.

There are two cases in the long division method based on the first digit of the dividend. Now, let’s learn about those cases in detail. 

Case 1: When the first digit of the dividend is greater than or equal to the divisor

Now let’s learn how to divide a number when the first digit of the dividend is greater than or equal to the divisor. For example, divide 252 by 2.

Step 1: Check if the dividend is less than or equal to the divisor from the left-hand side. Here, the first digit is 2 and it is equal to the divisor. 

Step 2: As 2 × 1 = 2, the quotient is 1.  

Step 3: The difference between the multiple of the divisor and the first digit, that is, 2 − 2 = 0.

Step 4: Now we will bring down the next digit (5), forming 05. Divide 5 ÷ 2 = 2, remainder is 1 (since 2 × 2 = 4, 5 – 4 = 1). The quotient digit is 2.

Step 5: Follow the steps till the remainder is 0 or less than the divisor. 

So, Continuing, bring down the next digit (2), forming 12. Divide 12 ÷ 2 = 6, 12 – 12 = 0. Thus, 252 ÷ 2 = 126, remainder is 0.

Case 2: When the first digit of the dividend is less than the divisor

In this section, let’s learn how to divide a number when the first digit of the dividend is less than the divisor. For example, dividing 235 by 5.

Step 1: If the first digit of the dividend is less than the divisor, that is, when dividing 235 by 5, where 2 is less than the divisor 5, we cannot divide it. So, we need to divide the first two digits, that is 23 by 5.

Step 2: As 5 × 4 = 20, the quotient is 4, and the leftover is 23 − 20 = 3. 

Step 3: Bringing down the next digit which is 5, next to 3, so the new dividend is 35.

Step 4: Repeat the steps till the remainder is 0 or less than the divisor. 


Here, the quotient is 47, so 235 ÷ 5 = 47