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

Hi.

In question, they gave a greatest number, in the sense.

Ex- if you take 4 as a greater num for the given question.

Means this is the greater num which divides all the dividend if you take 5 it won't divide all' the dividends.

If they ask greater num -then take smaller num in the choices and divide all the dividends by that num if you get remainder same then that is the answer.

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 the 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.

Good explanation @Prashant.

Easy to understand. Thanks to all the given explanation.

Well done @Saurabh.

I understood the sum now.

Given explanations was good. Thankyou all.

Why can't we think like this, In given four option one is HCF of 43, 91, 183. And leave the same reminder as per the question.

Let me consider 4 is HCF then divide the numbers by four. It shows the same reminder hence 4 is the answer.

Well explained, thanks @Prashant.

Here, the remainder is unknown that is why we have only chance to find their difference.

@Prashant.

In your explanation, 'p' must be a Divisor, not the Dividend.