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. 4)
4.
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
4
5
6
8
Answer: Option
Explanation:

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

  = H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

Discussion:
158 comments Page 11 of 16.

Ayush said:   1 decade ago
If two number gives same remainder when divided by a number (say N) then their diff will be perfectly divisible by that number (N).

Example 23 and 49 gives same remainder 1 when divided by two.

So the difference 49-23 = 26 is perfectly divisible by 2.

So our question suffices to finding the HCF of the differences. (Since we need the greatest number).

Hope now it is clear for all.

Pavan said:   1 decade ago
The reason they're taking the HCF of the difference of the numbers is because it's said that the numbers give equal remainder on being divided. So number n%p=q [% denotes remainder operation] and n1%p=q.

So (n1-n) %p=0. We can say that the number (p) is a factor of the difference of the two numbers.

Shrinivasmutagar said:   1 decade ago
3360 = 2*2*2*2*3*7*10.
2240 = 2*2*2*2*2*7*10.
5600 = 2*2*2*2*5*7*10.

HCF = 2*2*2*2*7*10 = 1120.

How this is done can any one explain?

Renu said:   1 decade ago
Hey can anyone tell how to find HCF fast for big numbers?

Mukesh priye said:   10 years ago
Common no. of each row is 22227 & 10 hence multiple of that Product equal to 1120.

Himank said:   10 years ago
@Shrinivasmutagar.

HCF is calculated by seeing the common factors in all the numbers.

For Ex: 2, 2, 2, 2, 7 and 10 is present in all the numbers.

And on * you will get 1120.

Rekha kharode said:   10 years ago
Please explain if someone knows why select only HCF?

Neha said:   10 years ago
How 1120?

Munsur said:   9 years ago
Will anyone explain the logic behind the Division Method of Finding HCF or GCD?

Niki said:   9 years ago
Thank you @Srinivas.


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