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Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case.

Solution:
Your problem -> Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case.

The number divides 1354 and leaves 10 as remainder
:. The number exactly divides 1354 - 10 = 1344

The number divides 1806 and leaves 10 as remainder
:. The number exactly divides 1806 - 10 = 1796

The number divides 2762 and leaves 10 as remainder
:. The number exactly divides 2762 - 10 = 2752

Now, we have to find HCF of 1344, 1796, 2752

Find HCF of 1344,1796,2752

1. Find HCF of (1344,1796)

 1

1344|
 1 7 9 6
|
 1 3 4 4

 2
|

|
 4 5 2
|
 1 3 4 4
|
 9 0 4

 1
|

|
 4 4 0
|
 4 5 2
|
 4 4 0

 3 6
|

|
 1 2
|
 4 4 0
|
 3 6
|
|
 8 0
|
 7 2

 1
|

|
 8
|
 1 2
|
 8

 2
|

|
 4
|
 8
|
 8
|
|
 0

HCF of (1344, 1796) = 4

2. Now find HCF of 4 and 3^(rd) number 2752

 6 8 8

4|
 2 7 5 2
|
 2 4
|
|
 3 5
|
 3 2
|
|
 3 2
|
 3 2
|
|
 0

HCF of (4, 2752) = 4

:. HCF of given numbers (1344,1796,2752) = 4

:. Required number = HCF of 1344, 1796, 2752 = 4.

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