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 8 of 16.
Nagarjuna D said:
1 decade ago
I can't understand why we have to subtract one among other?
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.
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.
Sai krishnan K said:
1 decade ago
Why it is not taken 5. It also gives the same remainder 0.
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.
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.
Ramana said:
1 decade ago
Thanks saraswathi. I get answer for this types of problems by following your explanation. Thanks a lot.
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).. :)
Rangan said:
1 decade ago
@Ramana : The Greatest common divisor (or the HCF) is not the solutiom needed here, it is rather the SUM OF THE DIGITS of THE HCF.
The Remainder being the same for each case, it is clear that subtracting the lesser no. from the greater ones renders the remainder zero. Also the HCF of te no.s left thereafter just wait to be known, because it perfectly divides the no.s and thus gets the same remainder in each case.
The Remainder being the same for each case, it is clear that subtracting the lesser no. from the greater ones renders the remainder zero. Also the HCF of te no.s left thereafter just wait to be known, because it perfectly divides the no.s and thus gets the same remainder in each case.
Gargi said:
1 decade ago
5 is not correct answer. As question is for sum of the greatest devider. And greatest number which devides all the given numbers is : 1120 so, digit sum of the same is 4.
Correct answer is: 4.
Correct answer is: 4.
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