Math CentralQuandaries & Queries


Question from RAYA, a student:

if 4821x14y is an 8-digit number divisible by 72. How many values can x and y take?

HI Raya,

I can tell you three facts that will help you solve this problem.

  1. $72 = 9 \times 8$ and hence your 8-digit number must be divisible by $9$ and by $8.$

  2. An integer is divisible by $9$ if and only if the sum of its digits is divisible by $9.$

  3. An integer is divisible by 8 if and only if the number formed by its hundreds, tens and units digit is divisible by 8.


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