SEARCH HOME
 Math Central Quandaries & 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.

Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.