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.
4
7
9
13
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:
210 comments Page 4 of 21.

Mozammil anwar said:   6 years ago
4/43 = remainder is 3.
4/183 =remainder is 3.
4/91 = remainder is 3.
So that' why the answer is 4.
(1)

Lokesh said:   6 years ago
Why we have to use hcf?

Bala said:   6 years ago
@All.

They asked to divide by a number also we need to have the same remainder in all cases.

So, dividing by 4, we get remainder 3 in all cases.
(1)

Pinku said:   6 years ago
43/4 = 3(remainder).
91/4 = 3(remainder).
183/4 = 3(remainder).

Pabitra Saha said:   6 years ago
Very good explanation, Thanks @Kuldeep Sharma.

Kuldeep Sharma said:   7 years ago
let the greatest number is H.

Now;

H*Quotient(Q1)+Reminder(R)= 43 -------> (1)
H*Quotient(Q2)+Reminder(R)= 91 -------> (2)
H*Quotient(Q3)+Reminder(R)= 183 -------> (3)
Now, (1)-(2), (3)-(2), (3)-(1)
H*(Q2-Q1)= 48,
H*(Q3-Q2)= 92,
H*(Q3-Q1)= 140.

So 48, 92 and 140 are completely divisible by H, that will be the HCF of these numbers.
So, the HCF of 48, 92 and 140 is 4.
(3)

Davoas said:   7 years ago
What if we have a fixed remainder.

For example take 90, 114 and 230 with remainder 6 what will be the divisor?

Anyone explain me.

Magnus Udoka said:   7 years ago
Your explanation was superb, Thanks @Prashant.

Shreekanth said:   7 years ago
Keep on dividing all the three numbers by 2 so that reminder should be the same ie
2[43 91 183]
[ 21 45 91] remainder will be 1 for all the three.

Divide again by 2.
2[21 45 91]
10 22 45 remainders will be same ie 1.

So after this, if you try to divide all three again by 2 then you get a different value for the reminder.
And hence; 2 * 2 = 4.
(1)

Pabitra Bhusan Saha said:   7 years ago
Your explanation is very easy to understand and this is the best process, Thanks @Saroja and @Sourav.


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