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1. What is difference between the smallest and largest \(5\)-digit numbers divisible by \(11?\)

 

2. What is the least positive integer \(n\) such that \(1560\) divides \(n!?\)

 

3. The six-digit integer \(789,XYZ\) consists of six distinct digits and is divisible by \(7, 8\) and \(9.\) What is the three-digit integer \(XYZ?\)

 

4. There is a number formed by \(n\) copies of \(2020\) and \(1\) in the unit place\(.\) If this number is divisible by \(11,\) what is the smallest possible value of \(n?\)

 

5. Modify one digit in the number \(31743\) can make it a multiple of \(823.\) What is the number after change\(?\)

 

(prob be posting these daily)
(not my homework)

 Apr 21, 2021
 #1
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1 - The smallest 5-digit integer is: 10010.  The largest 5-digit integer is: 99990

 

2 - The least positive integer n = 13

 

3 - The three-digit integer XYZ = 264

 

4 - The smallest possible value of n = 3: 202020202021 mod 11 = 0

 

5 - Change 31743 to 31274 mod 823 = 0

 Apr 21, 2021
 #2
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tysm!!!
i know the answers but.. still

edit: forgot to mention that #4 and #5 is wrong :(
        i won't tell you the answer just in case someone else answers but....

mworkhard222  Apr 21, 2021
edited by mworkhard222  Apr 21, 2021

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