Example:

Step 1: Let’s enter 12361236 in the calculator
Step 2: 12361236 is divisible by 137
Step 3: Now divide the result by the four-digit number
90228 / 1236

The result is 73!

The trick:

• Entering a four-digit number twice means multiplying the four-digit number by 10001.

  Example: 1236 x 10001 = 1236 x (10000 + 1)
  = 1236 x 10000 + 1236 x 1
  = 12360000 + 1236
  = 12361236

• Since 10001 = 73 x 137, it is always divisible by 137.

• If you divide 12361236 by 137, the remainder will be the product of 73 and the four-digit number.

• If you divide the remainder by the four-digit number, the remainder will always be 73. Simple!