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Does exist a natural number, which divided by 18, to give the reminder 11 and divided...

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emylemonslice | Student, Grade 9 | eNotes Newbie

Posted June 2, 2009 at 8:28 PM via web

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Does exist a natural number, which divided by 18, to give the reminder 11 and divided by another natural number, to give the quotient 27 and reminder6

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giorgiana1976 | College Teacher | Valedictorian

Posted June 3, 2009 at 3:07 AM (Answer #1)

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We'll write the rule of division with reminder:

D=d*q+r

D=dividend, d-divisor, q-quotient, r-reminder

Let's suppose that our natural number is x.

x=18*q+11

x=d*27+6

18*q+11=d*27+6

d*27+6-18*q=11

We notice that we have the common factor 3, which we'll draw out  and we'll rewite the expression above:

3*(9*d+2-6*q)=11

It's more than clear that nor 3, either paranthesis, are not  11's divisor, so the conclusion is that it doesn't exist a natural number to have the properties enunciated above!

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