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

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.

I can't understand the question.

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

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.

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.

Assume that the required answer is "D" and the remainder that it leaves when dividing 43, 91 and 183.

This means that,

43 = d*q1 + r,

91 = d*q2 + r,

183 = d*q3 + r,

Where q1, q2 and q3 are the respective quotients.

Subtracting the first equation from second, we get:

91 - 43 = (d*q2 + r) - (d*q1 + r).

Hence, 48 = d*(q2 - q1) = d*(an integer).

Similarly, subtracting second equation from first, we get:

183 - 91 = (d*q3 + r) - (d*q2 + r).

Hence, 92 = d*(q3 - q2) = d*(another integer).

Now, 48 = d*(an integer) and 92 = d*(another integer) mean that both 48 and 92 are divisible by d. (In other words, "d" is a common divisor of 48 and 92. )

Now common divisors of 48 and 92 are 1, 2 and 4 only. Out of which, highest is 4. (Alternatively, you can directly find the HCF (or GCD) of 48 and 92). Hence 4 is the answer.

Note:

There is no need to calculate the HCF of 3 numbers, namely (91 - 43), (183 - 91) and (183 - 43). It is sufficient to take any two of these three numbers. The HCF will still be 4.

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

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

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?

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