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

TO FIND THE HCF OF TWO NUMBERS,

DIVIDE THE BIGGER NUMBER BY SMALLER .

TAKE 2032 AND 1651, ON DIVIDING.

1651)2032( 1
1651
--------------
381
-------------
THEN DIVIDE 1651 BY 381.

381)1651(4
1524
--------------
127
--------------
THEN DIVIDE 381 BY 127.

127)381(3
381
----------
0
----------
THE DIVIDING OF BIGGER NUMBER BY SMALLER NUMBER SHOULD CONTINUE TILL WE GET REMAINDER AS ZERO.

THEN THE LAST DIVISOR IS THE H.C.F OF THE TWO GIVEN NUMBERS.

Thank you mr. M. V. Krishna/Palvoncha.

It is not possible .
the term 1657+6 is not a perfet multiplier it gives a remainder 1.the term 1657-6 is a perfect multiplier it gives a remainder 0.that's why they doesnot give same answer.

No .it is not possible .because 1657-6 gives the remainder 0,but 1657+6 gives the remainder 1.

Can we do 1657+6 or 1657-6 both will give same answer. ?

THANKS krishna your explanation is too easy.

Here 6 & 5 are remainders of 1657(say A) & 2037(say B) respectively.

To make A and B(dividends) perfectly divisible by a divisor, the remainders should be subtracted from dividends.

Now if we divide the dividend by a divisor, the remainder will be zero, because we made dividends perfectly divisible.

Now the numbers are 1657-6=1651 and 2037-5=2032.

HCF of 1651,2032.

1651)2032(1
1651
-------
381)1651(4
1524
------
127)381(3
381
------
0
-------
So HCF is 127.

Hope you understand.

Ho we know that 1657 - with 6 and how we know that 2037 is minus with 5 please explain.

Division Method: Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

ans...

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of 1651 and 2032
let devide the greater no with smaller one means
2030/1651=381
then,1651/381=127
then,381/127=0

so the
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:127

HCF Explain & give me some examples please.