Question

find the greatest number which divided 247 and 2055 leaving remainders 7 in each case​

Answer 1

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

Step - 1 : Subtract 7 from each case.

》247 - 7 = 240

》2055 - 7 = 2048

Step - 2 Find HCF of 240 and 2048

240 ,

3 | 240

2 | 80

2 | 40

2 | 20

5 | 10

2 | 2

2048 ,

2 | 2048

2 | 1024

2 | 512

2 | 256

2 | 128

2 | 64

2 | 32

2 | 16

2 | 8

2 | 4

2 | 2

Calculating,

240 = 2 × 2 × 2 × 2 × 5 × 3

2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

In common = 2 × 2 × 2 × 2

Hcf = 16

Hence, the greatest number will be 16

Answer 2

$\bold{Answer}$

Step - 1 : Subtract 7 from each case.

》247 - 7 = 240

》2055 - 7 = 2048

Step - 2 Find HCF of 240 and 2048

240 ,

3 | 240

2 | 80

2 | 40

2 | 20

5 | 10

2 | 2

2048 ,

2 | 2048

2 | 1024

2 | 512

2 | 256

2 | 128

2 | 64

2 | 32

2 | 16

2 | 8

2 | 4

2 | 2

Calculating,

240 = 2 × 2 × 2 × 2 × 5 × 3

2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

In common = 2 × 2 × 2 × 2

Hcf = 16

Hence, the greatest number will be 16