Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

required no.=h.c.f of(91-43),(183-91) and (183-43) =h.C.F OF 48,92 and 140=4 hence A option is correct could u please explain this mthod in detail? would much appreciate the help. The answer is 4 and how it is 4 is below, We can represent any integer number in the form of: D*q + r. Where D is divisor, q is quotient, r is remainder. so each number can be written accordingly: 43 = D*q1 + r1; 91 = D*q2 + r2; 183 = D*q3 + r3; r1,r2 & r3 will be same in above three equations according to the question. D is the value that we want to find out. which should be greatest. On solving three equations we get: D*(q2-q1)= (91-43)=48 D*(q3-q2)= (183-91)=92 D*(q3-q1)= (183-43)=140 It is obvious that q3>q2>q1 For the greatest value of D that divide each equation we take the HCF of 48,92,140 THEREFORE ANSWER IS 4. Please give kudos !! Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case. A. 4 B. 7 C. 9 D. 13 E. 24 This question lends itself to testing the answer choices Since we're looking for the greatest number, we'll start at E and work our way to A E) 24 43 divided by 24 equals 1 with remainder 19 91 divided by 24 equals 3 with remainder 19 183 divided by 24 equals 7 with remainder 15 We need the SAME remainder each time - ELIMINATE E D) 13 43 divided by 13 equals 3 with remainder 4 91 divided by 13 equals 7 with remainder 0 We need the SAME remainder each time - ELIMINATE D C) 9 43 divided by 9 equals 4 with remainder 7 91 divided by 9 ...

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case. A. 4 B. 7 C. 9 D. 13 E. 24 This question lends itself to testing the answer choices Since we're looking for the greatest number, we'll start at E and work our way to A E) 24 43 divided by 24 equals 1 with remainder 19 91 divided by 24 equals 3 with remainder 19 183 divided by 24 equals 7 with remainder 15 We need the SAME remainder each time - ELIMINATE E D) 13 43 divided by 13 equals 3 with remainder 4 91 divided by 13 equals 7 with remainder 0 We need the SAME remainder each time - ELIMINATE D C) 9 43 divided by 9 equals 4 with remainder 7 91 divided by 9 equals 10 with remainder 1 We need the SAME remainder each time - ELIMINATE C B) 7 43 divided by 7 equals 6 with remainder 1 91 divided by 7 equals 13 with remainder 0 We need the SAME remainder each time - ELIMINATE B By the process of elimination, the correct answer is A RELATED VIDEO _________________

Hint: Represent the number as $\text$ or $4$ is the highest common factor between 48, 92, 140. So the value of d or divisor is $4$ . The correct option is “A”. Note: In such types of problems we need to find the factors of given numbers. Here the remainder is the same and we have 3 equations and 3 variables. After solving these 3 equations we get the value of the divisor which is represented by d.