Question

Find the greatest number which can divide 284,698 and 1618 leaving the same remainder 8 in each case.

Answer 1

$\sf\underline{Step-by-step \: explanation}$

Step - 1 : Subtract 8 from each case

》284 - 8 = 276

》698 - 8 = 690

》1618 - 8 = 1610

Step - 2 Find the Hcf of subtracted observations

276,

3 | 276

2 | 92

2 | 46

23 | 23

276 = 3 × 2 × 2 × 23

690,

5 | 690

3 | 138

2 | 46

23 | 23

690 = 5 × 3 × 2 × 23

1610,

5 | 1610

2 | 322

23 | 161

7 | 7

1610 = 5 × 2 × 23 × 7

Calculating,

276 = 3 × 2 × 2 × 23

690 = 5 × 3 × 2 × 23

1610 = 5 × 2 × 23 × 7

In common = 2 × 23

Hcf = 46

Hence, 46 in the required number

Answer 2

$\bold{Answer}$

Step - 1 : Subtract 8 from each case

》284 - 8 = 276

》698 - 8 = 690

》1618 - 8 = 1610

Step - 2 Find the Hcf of subtracted observations

276,

3 | 276

2 | 92

2 | 46

23 | 23

276 = 3 × 2 × 2 × 23

690,

5 | 690

3 | 138

2 | 46

23 | 23

690 = 5 × 3 × 2 × 23

1610,

5 | 1610

2 | 322

23 | 161

7 | 7

1610 = 5 × 2 × 23 × 7

Calculating,

276 = 3 × 2 × 2 × 23

690 = 5 × 3 × 2 × 23

1610 = 5 × 2 × 23 × 7

In common = 2 × 23

Hcf = 46

Hence, 46 in the required number