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

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

(1305 - 4665) = 3360.
(4665 - 6905 ) = 2240.
( 6905 - 1305) = 5600.

Then HCF Of 3360 - 3 * 1120,
HCF Of 2240 - 2 * 1120,
HCF Of 5600 - 5 * 1120,
Sum Of Digits in N = 1 + 1 + 2 + 0 = 4.


I hope it's easy to understand.

If we only take two differences i.e. 6905 - 4665 = 2240, 4665 - 1305 = 2360.
HCF of 2240 and 2360 is 40.
4+0 = 4.

Why should we subtract the Numbers with the smallest number and so HCF for that?

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.

How do you get 4? I am not getting it clearly.

I can't understand this question properly.

So, please If anybody knows properly it. Please explain it.

I'm also not getting it please anyone can explain in detail?

The main thing is why should we subtract those numbers is there any trick?

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.

1305÷1120 leaves 185 as the remainder
4665÷1120 leaves 185 as the remainder
6905÷1120 leaves 185 as the remainder.

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

I can't understand. Why should we subtract the numbers?