Question

the largest number which divides 71 and 97 leaving remainder 11 and 7 respectively

Answer 1

Hi,

Here's ur answer :-

According to the question, if 71 and 97 are divided by a certain number, there will be certain remainders.

So, this statement shows that the remainder is extra value in the given numbers and are to be subtracted.

71-11= 60
97-7=90

As, they are to be divided by the same but largest possible number, we have to take the HCF of 60 and 90.

60 = 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5

Common = 2 x 3 x 5 = 30

So, the required number is 30.

HOPE IT HELPS (^_^)

Answer 2

Heya user,

Given the no.s 71 and 97....
Let's say the required no. is 'x' ...

So, the question asks that x must divide 71 to leave a remainder 11..
which means 71 is 'x' times something plus 11.. which in Mathematical Terms can be written as :->
----> 71 = ax + 11;
----> ( 71 - 11 ) = ax
==> ax = 60 <---  (i)
------[ Don't be confused c'oz 'a' is just any integer introduced ]

Similarly,
---> 97 = bx + 7 <-- [ b times x plus 7 where b is just any no. ]
==> bx = 90 <--- (ii)

From (i) and (ii), and According to our question, -->
---> What can be the maximum value of 'x' that satisfies both (i), (ii)-->

Soo, we find HCF ( 60, 90 ) which is equal to --> 30
And hence, x = 30 is the Required no. which satisfies both (i) (ii) as well as the Demand of the Question......

Hope you got an Understanding as to how to use HCF concepts for such Tricky Qns.......