Long division on large numbers is performed by breaking down the number being divided, also known as the dividend, by place value. The digits of the dividend are treated as individual long division problems, with the remainder successively carrying over to the next digit being worked, until the smallest place value in the dividend is reached.
To solve a problem using long division, the divisor is first multiplied to find the closest whole number product to the dividend. The number multiplied with the divisor is placed over the dividend, and then the product is subtracted from the dividend. If the product and the dividend are identical, the result of the subtraction is zero, and the long division problem is considered solved. The number over the divisor is the answer to the problem.
If the result is not zero, the result of this subtraction is called the remainder. The remainder may be retained as a separate number or subjected to further division.
In a long division problem involving large numbers, such as 7680 divided by 30, the process is started by treating the initial digit of the dividend as if it were an individual number. This digit is divided, and the remainder is carried over and added to the next digit in the dividend. Then this number is divided in turn.
Division continues from the largest place value to the smallest, with the remainder being carried over and summed to the next digit in each step. When the smallest place value in the dividend is reached, the problem is considered solved if the result of the final subtraction is zero. If the result is not zero, the remainder of this division may either be retained or subjected to further division until a result of zero is finally obtained.