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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|
1796
 |
1344
 
2
 |
 
 |
452
|
1344
|
904
 
1
|
 
|
440
|
452
|
440
 
36
|
 
|
12
|
440
|
36 
|
|
80
|
72
 
1
|
 
|
8
|
12
|
8
 
2
|
 
|
4
|
8
|
8
|
|
0

HCF of (1344, 1796) = 4

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

  
688
  
4|
2752
 |
24  
 |
 |
35 
 |
32 
 |
 |
32
 |
32
 |
 |
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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