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

If the sum of two numbers are 348 and their HCF is 48 then what is the difference of the numbers?

Please tell me the most simple formula.

Here in this question greatest number is 7 and it gives the same remainder that is 1 when divided by all. So how is the answer 4?

In @Prasanth answer, p is the divisor not dividend and the analysis of sum is correct.

Yes your right @Sowjanya. But @Prasanth is almost right I think you need more information.

1st divide 48 with 4 then remainder is 0.

2nd divide 92 with 4 then remainder is 0.

3rd divide 140 with 4 then remainder is 0.

Hence so 4 is a perfect number.

Easy calculation, 7 and 13 are directly eliminated.

4 and 9 are the required. So divide it by the 9, no remainder will be same. So 4 is the option.

How to solve the same question if remainder is not same in each case?

I can't understand the question.

An indirect way to understand.

Let's take the numbers are 28, 35, 56 and the divisor is 7.

When 7 divide these remainder are 0, 0, 0.

Now see 35 - 28 = 7, (Divisible by divisor). Also 56 - 28 = 28 and 56 - 35 = 21 both are divided by divisor. This is like property check for any number.

So we can use this in our problem. Two or more no. when giving the same remainder with common divisor then the difference between the original numbers are also divided by divisor.

Further using in question. 91, 43, 183. See we don't have divisor or factor.

See d or factor divide the no 91, 43, 183 and the differences.

91 - 43, 183 - 43, 183 - 91 say 48, 140, 92.

Since any common divisor or heresy HCF should divide the numbers and differences so we find the HCF of 48, 140, 92.

Hope this will clear why we take difference.