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:
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 13 of 16.
Anchit said:
1 decade ago
We are taking hcf of (4665 - 1305) , (6905 - 4665) and (6905 - 1305)..because in this way the remainder is cancelled...
take an example..
12 and 7..both give remainder 2 when divided by 5.
now when we substact (12-7) the differance 2 is cancelled ...
hence we get a number that is completely divisible i.e a factor of 5..(or the hcf).. :)
take an example..
12 and 7..both give remainder 2 when divided by 5.
now when we substact (12-7) the differance 2 is cancelled ...
hence we get a number that is completely divisible i.e a factor of 5..(or the hcf).. :)
Ramana said:
1 decade ago
Thanks saraswathi. I get answer for this types of problems by following your explanation. Thanks a lot.
Sanatan said:
1 decade ago
The answer is actually 5 and is pretty simple. You can see by dividing the given numbers by 5 we get the same remainder zero as asked in the question.
As we have to find the max number which yields the same remainder for the given numbers. 4 is not the correct answer here.
As we have to find the max number which yields the same remainder for the given numbers. 4 is not the correct answer here.
M.Harish said:
1 decade ago
1305, 4665, 6905 ----- These are the numbers.
In this question why we subtract the numbers because here it is said that they have same remainder.
So, 1305 = hcf * x + remainder.
4665 = hcf * y + remainder.
6905 = hcf * z + remainder.
Where x, y, z are respective quotients.
So. When we subtract those numbers, they become multiples of the hcf. Then we can directly calculate hcf.
In this question why we subtract the numbers because here it is said that they have same remainder.
So, 1305 = hcf * x + remainder.
4665 = hcf * y + remainder.
6905 = hcf * z + remainder.
Where x, y, z are respective quotients.
So. When we subtract those numbers, they become multiples of the hcf. Then we can directly calculate hcf.
Sai krishnan K said:
1 decade ago
Why it is not taken 5. It also gives the same remainder 0.
Alisha (Alice) said:
1 decade ago
HCF (Highest Common Factor) is also known as GCD (Greater Common Divisor).
And, there are various ways through which one can find HCF of the given numbers. Among these, one of the methods is well explained by Yogesh and another by Saraswati.
And, there are various ways through which one can find HCF of the given numbers. Among these, one of the methods is well explained by Yogesh and another by Saraswati.
Rajeswari R said:
1 decade ago
@Madhu. They didn't mention exactly n divide these 3 numbers. They said when dividing it will leaves remainder please consider that part.
Nagarjuna D said:
1 decade ago
I can't understand why we have to subtract one among other?
Sat said:
1 decade ago
Yogesh is pretty much right.
Smilly siva said:
1 decade ago
Hey anyone here can please expain me why we take hcf of (4665 - 1305) , (6905 - 4665) and (6905 - 1305). ? please give explaination.
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