# Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 1)

1.

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

Answer: Option

Explanation:

Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

= H.C.F. of 48, 92 and 140 = 4.

Discussion:

200 comments Page 20 of 20.
Shwetha said:
1 decade ago

Simply divide each number by 4 the remainder is same for all so the answer is 4.

Hary said:
1 decade ago

Solving the equations:

91=pq2+r

43=pq1+r

_________________

48=pq2-pq1

thus

48=p(q2-q1)=91-43.

91=pq2+r

43=pq1+r

_________________

48=pq2-pq1

thus

48=p(q2-q1)=91-43.

Sakthivel said:
1 decade ago

How to arrive at this equation p(q2-q1)= (91-43) from 43 = pq1 + r;

91 = pq2 + r;

183 = pq3 + r;

91 = pq2 + r;

183 = pq3 + r;

Prashant said:
1 decade ago

We can represent any integer number in the form of: pq+r.

Where p is dividend, q is quotient, r is reminder.

so: 43 = pq1 + r;

91 = pq2 + r;

183 = pq3 + r;

Take r same in above three equations as given in question.

p is the value that we want to find out. which should be greatest.

On solving three equations we get:

p(q2-q1)= (91-43)=48;

p(q3-q2)= (183-91)=92;

p(q3-q1)= (183-43)=140;

For the greatest value of p that divide each equation we take the HCF of 48,92,140

THEREFORE ANSWER IS 4.

Where p is dividend, q is quotient, r is reminder.

so: 43 = pq1 + r;

91 = pq2 + r;

183 = pq3 + r;

Take r same in above three equations as given in question.

p is the value that we want to find out. which should be greatest.

On solving three equations we get:

p(q2-q1)= (91-43)=48;

p(q3-q2)= (183-91)=92;

p(q3-q1)= (183-43)=140;

For the greatest value of p that divide each equation we take the HCF of 48,92,140

THEREFORE ANSWER IS 4.

Arya said:
1 decade ago

If three nos as in this case is 43, 91 and 183 are given then to find HCF the shortest solution is take the diff:

1) 91 - 43 = 48 (4*3*7)

2) 183 - 91 = 92 (4*23)

3) 183 - 43 = 140 (4*7*5)

Thus the HCF is 4.

1) 91 - 43 = 48 (4*3*7)

2) 183 - 91 = 92 (4*23)

3) 183 - 43 = 140 (4*7*5)

Thus the HCF is 4.

Anirudh rai said:
1 decade ago

Is this the only way to this type of problem?

If yes then would you please explain it.

If yes then would you please explain it.

Raj said:
1 decade ago

Why do we do the difference of number to each other?

Sourabh Das said:
1 decade ago

I also want an explanation about the logic of the solution.

Anu said:
1 decade ago

Explain the logic of this solution.

Nagu said:
1 decade ago

Why they took difference between those nos.

Please explain me.

Please explain me.

Post your comments here:

Quick links

Quantitative Aptitude

Verbal (English)

Reasoning

Programming

Interview

Placement Papers