Question

69. Find the largest number which divides 34, 58 and
94 leaving the same remainder in each case.​

Answer 1

Answer:

the largest number 2 divided 34,58 & 94

Answer 2

12 is the largest number which divides 34, 58 and 94 leaving the same remainder in each case.​

Given,

Three numbers: 34, 58, and 94

To Find,

The largest number which divides 34, 58, and 94 leaving the same remainder in each case.

Solution,

The method of finding the largest number which divides 34, 58, and 94 leaving the same remainder in each case is as follows -

Let the largest number which divides 34, 58 and 94 leaving the same remainder in each case is d and the common remainder is r.

Then, 34 - r, 58 - r, and 94 - r are divisible by d.

Then, $(58-r) - (34 - r)=24$ and $(94-r)-(54-r)=60$ are also divisible by d.

Since 24 and 60 are divisible by d, the highest possible number possible as the value of d is the highest common factor of 24 and 60.

The highest common factor of 24 and 60 is 12.

Hence, the largest number which divides 34, 58 and 94 leaving the same remainder in each case is 12.​

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