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
Answers
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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.
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