Set up the division problem normally with the divisor on the left side of the division and the dividend on the right side. The quotient will be formed on top of the dividend.
Choose the first integer of the dividend. If the first integer is not larger than the divisor, then choose the first two integers. For example, if dividing 1345 by 8, choose 13.
Calculate how many whole times the divisor will go into the number from Step 2. In this case, 8 goes into 13 one time with a remainder of 5.
Write the remainder from Step 3 next to the number from Step 2 in superscript. In this example, the process yields 13(^5)45. This is where short division saves time over long division. Instead of writing out "13-8 = 5" below the dividend and carrying down the next integer, the steps are done mentally.
Append the next number to the superscript, and calculate how many times the divisor goes into the number. In this case, "^5" and "4" yields 54. And, 8 goes into 54 six times.
Repeat steps 3 through 5 until all of the integers in the dividend have been used. The final remainder of the process is the remainder of the entire division. In this example, the final result is 168 with a remainder of 1.