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3. In dividing a number by 585, a student employed the method of shรถrt division. iithe number successively by 5, 9 and 13 (factors of 585) and got the remainders 4, 8, 12respectively. If he had divided the number by 585, the remainder would have been |
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Answer» Let's take a look at your question. The question states that when the number is divided by 5 the remainder is 4.Let the number be x and q be the quotient, then x=5p+4−−−(i)x=5p+4−−−(i) The successive division by 9 result into the remainder 8. p=9q+8−−−(ii)p=9q+8−−−(ii) Similarly, the successive division by 13 result into the remainder 12. q=13r+12−−−(iii)q=13r+12−−−(iii) Now substitute value of q in eq(ii) p=9q+8p=9q+8 p=9(13r+12)+8p=9(13r+12)+8 p=117r+108+8p=117r+108+8 p=117r+116p=117r+116 Now replace this value of p in eq(i) x=5p+4x=5p+4 x=5(117r+116)+4x=5(117r+116)+4 x=585r+580+4x=585r+580+4 x=585r+584x=585r+584 Which represents that 585 is the divisor, r is the quotient and 584 is the remainder.Therefore, when the number is divided by 585, the remainder is 584. |
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