Question

Find the greatest number which when it divides 367, 135 and 259 will leave the same remainder in

each case.​

Answer 1

Answer:

Answer. Answer: The largest number would be 6. 150, 180, and 144. We need to find the largest number which divides the above numbers and leaves the same remainder in each case.

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Answer 2

Given:

The greatest number which when it divides 367, 135 and 259 will leave the same remainder in  each case.​

To find:

The greatest number

Solution:

(1). We are given 3 numbers 367, 135 & 259 each of which when divided by the greatest number gives the same remainder in each case which is not given to us.

(2). So, we will find the difference between each pair.

367 - 135 = 232

367 - 259 = 108

259 - 135 = 124

(3). Now we will find the H.C.F. of 232, 108 & 124 by using the prime factorisation method

232 = 2 × 2 × 2 × 29

108 = 2 × 2 × 3 × 3 × 3

124 = 2 × 2 × 31

∴ H.C.F. (232, 108 & 124) =  2 × 2 = 4

Thus, the greatest number which when it divides 367, 135 and 259 will leave the same remainder in  each case is → 4.

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