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| Math Central | Quandaries & Queries |
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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.
- $72 = 9 \times 8$ and hence your 8-digit number must be divisible by $9$ and by $8.$
- An integer is divisible by $9$ if and only if the sum of its digits is divisible by $9.$
- 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
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