Question

1. Find the largest number which divides 1280 and 1371 leaving a remainder 6 in each case .


2.Find the greatest number that will divide 76. 113 and 186 leaving remainder 4,5,6 respectively.

Please answer thus question .
1. Answer is 91
2.Answer is 36
but I want solution
please​

Answer 1

1)

Firstly we will do,

=> 1280 - 6 = 1274

=> 1371 - 6 = 1365

Hence the required number is the HCF of 1280 and 1371.

Therefore: HCF of 1280 and 1371 is 91.

Hence the required number is the HCF of 1280 and 1371 that is 91.

2)

=> 76 - 4 = 72

=> 113 - 5 = 108

=> 186 - 6 = 180

Now, find the greatest common factor of these numbers:

=> 72 = 2 x 2 x 2 x 3 x 3

=> 108 = 2 x 2 x 3 x 3 x 3

=> 180 = 2 x 3 x 3 x 2 x 5

Common factors are: 2 x 2 x 3 x 3 = 36

HCF{72,108,180}

So, 76/36 = 2 => remainder is 4

113/36 = 3 => remainder is 5

186/36 = 5 => remainder is 6.