Smallest Number for Divisibility

We need to find the smallest number that, when added to 71079, makes the sum perfectly divisible by 23.

Division Calculation

First, divide 71079 by 23 to determine the remainder.

$ 71079 \div 23 $

Performing the long division or using a calculator:

$ 71079 = 23 \times 3090 + 9 $

The remainder is 9.

Number to Add Calculation

The remainder of 9 indicates that 71079 is 9 more than a multiple of 23.

To reach the next multiple of 23, we need to add the difference between the divisor (23) and the remainder (9).

Number to add = $ 23 - 9 $

Number to add = $ 14 $

Verification Step

Add the calculated number (14) to the original number:

$ 71079 + 14 = 71093 $

Check if the new sum (71093) is divisible by 23:

$ 71093 \div 23 = 3091 $

The division yields a whole number, confirming divisibility.

Final Answer

The smallest number that should be added to 71079 is 14.