# 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:
150 comments Page 1 of 15.

Shuvojoti said:   5 months ago
What is it exactly saying, when it says, "leaving the same remainder"?

We are ultimately finding the HCF, right? Then what is it defining by "Same remainder"?

Anyone, please explain me this in detail.
(3)

Jai said:   6 months ago
Given numbers 1305, 4665, 6905.

Now take difference;
4665 - 1305 = 3360,
6905 - 4665 = 2240,
6905 - 1305 = 5600.
now,
Divide 3360/2240=1120, and
Now divide 5600/1120=0.
so, the HCF of 3360, 2240 & 5560 is 1120.
n=1+1+2+0=4;
So, n=4
(10)

Surya said:   8 months ago
Why should we subtract the Numbers with the smallest number and so HCF for that?
(10)

Suraj Chaudhary said:   10 months ago
I can't understand this question properly.

So, please If anybody knows properly it. Please explain it.
(10)

Gourav said:   12 months ago
@Anomi

Here, we need to find the greatest number. So 5 is not the greatest number.
(4)

Agondeze milly said:   1 year ago
How do you get 4? I am not getting it clearly.
(10)

Krishnakanth said:   1 year ago
Given numbers 1305, 4665, 6905.

Now take difference;
4665 - 1305 = 3360,
6905 - 4665 = 2240,
6905 - 1305 = 5600.

3360 factor it will give you 4,4,10,7 all divisible by the other 2 numbers.
So, multiple them and you will get 1120 add them because in question they said digits give you 4 i.e answer.
(15)

Sumit said:   2 years ago
If we only take two differences i.e. 6905 - 4665 = 2240, 4665 - 1305 = 2360.
HCF of 2240 and 2360 is 40.
4+0 = 4.
(19)

Ashu said:   2 years ago
Thanks for explaining @Saraswati.
(4)

Komal said:   2 years ago
Thank you for explaining the answer @Greeshma.
(2)

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