# 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
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:
148 comments Page 2 of 15.

Anomi said:   2 years ago
When these numbers are divided by 5 then the remainder is zero right. Then the Answer should be 5 right. Please explain to me.
(4)

Elissa said:   2 years ago
I understood well, thanks to all for explaining.
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Deeksha said:   3 years ago
Good, Thanks you @Greeshma.

K.snigdha shree said:   3 years ago
Thanks all for epxlaining.

Greeshma said:   3 years ago
Given numbers 1305, 4665, 6905.

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

Take the smallest difference i.e 2240 find factors of it;
1-> 2240
2-> 1120
4-> 560
5-> 448
and so on;

Check from highest factors if any one of them leaves the same remainder for all given numbers
So, 1st one 2240 it can't divide 1305. So, go for the second one 1120.

1305Ã·1120 leaves 185 as the remainder
4665Ã·1120 leaves 185 as the remainder
6905Ã·1120 leaves 185 as the remainder.

As all given conditions fulfilled :)
We got it;
1120.
1+1+2+0= 4.
Edits are welcome
(6)

Subhasis said:   3 years ago
Thanks @Saraswati.

Vineeth said:   3 years ago
Thanks all for explaining.

Minkel Aryan said:   3 years ago
Thanks all.

Babu said:   3 years ago
Thank you all.

Kezang Wanhchuk said:   3 years ago
@All.

The solution is;

=> 1305/4= remiander is .250, 4664/4= .250 and 6905/4= .250
1305/5= no remainder to all.
=> 1305/6= .50, 4665/6= .50 and 6905/6= .833(remainder is diferent)
=> 1305/8= .125 so, remainder is less.
Whereas we are finding HCF so less remainder is not HCF.
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