Question

1:
Find the greatest mumber 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​

Answer 1

Answer:

answer is 4

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Step-by-step explanation:

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.