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:
157 comments Page 16 of 16.

Merlinissac said:   10 months ago
4 * 1304 + 1 = 1305
4 * 4664 + 1 = 4665
4 * 6904 + 1 = 6905.
(3)

Sudha patil said:   9 months ago
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?
(13)

Nidhitiwari said:   9 months ago
Very good and helpful. Thanks all.
(2)

Vishnupriya Venkateshwaran said:   5 months ago
As explained in the question,

1305 = N(p) + r --->(1)
4665 = N(q) + r --->(2)
6905 = N(s) + r --->(3)

Now solve (2) - (1)=> 3360 = N (q-p) ---> (4)
and solve (3) - (2)=> 2240 = N (s-p) ---> (5)

Factorizing,
3360 = 1120 * 3 ---> (6)
2240 = 1120 * 2 ---> (7)

Comparing (4) and (5) with (6) and (7), we can clearly say that N=1120.
sum of digits in N = 1+1+2+0 = 4.
(1)

Arjun said:   4 months ago
Step 1: Differences between the numbers.

4665−1305 = 3360.
6905−4665 = 2240.
6905−1305 = 5600.

Step 2: Find the GCD of these differences
common prime factors are 2^5 . 5. 7 = 1120.

Step 3: Sum of the digits of 𝑁
1 + 1 + 2 + 0 = 4.
(1)

Chahat Mishra said:   2 months ago
@All. Here's my solution.

Num 1305, 4665, 6905.
Difference;
4665 - 1305 = 3360,
6905 - 4665 = 2240,
6905 - 1305 = 5600.
Now,
3360/2240 = 1120,
5600/1120 = 0.
HCF 3360, 2240 & 5560 is 1120.
n = 1 + 1 + 2 + 0 = 4;
So, n = 4.
(1)

Disha Mukherjee said:   2 months ago
I can't understand. Why should we subtract the numbers?
(8)


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