document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980124>Question 980124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi!good day.can you help me answering this question?<BR>\n" );
document.write( "1.The LCM of 84 and the number n is 588 and their GCF is 28.What is n?<BR>\n" );
document.write( "2.What is the smallest integers greater than 2014 that is divisible by 101?<BR>\n" );
document.write( "3.How many multiples of 16 are there between 100amd 1000?<BR>\n" );
document.write( "4.If 7n is divided by 5,the remainder is 3.Find the remainder when 3n is divided by 5?<BR>\n" );
document.write( "5.How many four digit numbers are multiples of 4 but not if 6?<BR>\n" );
document.write( "10.What is the smallest positive integers which when multiplied to 2014 will make it a perfect square?\r<BR>\n" );
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document.write( "I hope you can help me answering that questions.Thanks a lot. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601346 by </B><A HREF=/tutors/aboutme.mpl?userid=onlinepsa><B>onlinepsa(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onlinepsa><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=onlinepsa><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.The LCM of 84 and the number n is 588 and their GCF is 28.What is n?\r<BR>\n" );
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document.write( "For two natural numbers, their product = LCM * GCF.\r<BR>\n" );
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document.write( "Thus, n* 84 = 588 * 28<BR>\n" );
document.write( "=> n =(588* 4)/12 = 196\r<BR>\n" );
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document.write( "2.What is the smallest integers greater than 2014 that is divisible by 101?\r<BR>\n" );
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document.write( "When 2014 is divided by 101, Quotient: 19 Remainder: 95\r<BR>\n" );
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document.write( "Thus, when (Divisor - Remainder) or (101-95) or 6 is added to 2014, the latter becomes divisible by 19.\r<BR>\n" );
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document.write( "Answer= 2014+6 = 2020.\r<BR>\n" );
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document.write( "3.How many multiples of 16 are there between 100 and 1000?\r<BR>\n" );
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document.write( "16*7 = 112\r<BR>\n" );
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document.write( "16*62 = 992\r<BR>\n" );
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document.write( "Thus, there are 62-7+1= 56 multiples\r<BR>\n" );
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document.write( "4.If 7n is divided by 5,the remainder is 3.Find the remainder when 3n is divided by 5?\r<BR>\n" );
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document.write( "When 7n is divided by 5,the remainder is 3; let us try finding a value of n that satisfies the condition.\r<BR>\n" );
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document.write( "We can observe that if n=4, the number = 28. Remainder is 3 when 28 is divided by 5.\r<BR>\n" );
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document.write( "Now, 3n= 3*4= 12. Remainder when 12 is divided by 5 = 2.\r<BR>\n" );
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document.write( "5.How many four digit numbers are multiples of 4 but not if 6?\r<BR>\n" );
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document.write( "Multiples of 4: 1000, 1004, 1008, 1012, 1016, 1020 ...9996 ; \r<BR>\n" );
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document.write( "1000 = 4*250<BR>\n" );
document.write( "9996=  4*2499\r<BR>\n" );
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document.write( "Total multiples= 2499-250+1= 2500-250 = 2250\r<BR>\n" );
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document.write( "The multiples we have to exclude are those which are not divisible by 6.\r<BR>\n" );
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document.write( "Among the multiples whichever are divisible by 3 would be divisible by 6. Looking at the first few numbers we must notice that every third number (1008, 1020,...) are divisible by 3. \r<BR>\n" );
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document.write( "Thus out of 2250 multilples, 1/3rd would be those which are divisible by 6. \r<BR>\n" );
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document.write( "Therefore, 2250 - (1/3)*2250= 2250 - 750 = 1500 are those which are multiples of 4 but not multiple of 6.\r<BR>\n" );
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document.write( "Ans: 1500\r<BR>\n" );
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document.write( "10.What is the smallest positive integers which when multiplied to 2014 will make it a perfect square?\r<BR>\n" );
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document.write( "2014 = 2* 1007 = 2* 19* 53\r<BR>\n" );
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document.write( "As all 2,9 and 53 are prime numbers, we would need another 2, 19 and 53 to be multiplied to make it a perfect square. Thus, smallest positive integer to be multiplied is 2014 itself!\r<BR>\n" );
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