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The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder.

Solution:
Your problem `->` The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder.


The number divides 1657 and leaves 6 as remainder
`:.` The number exactly divides 1657 - 6 = 1651

The number divides 2772 and leaves 5 as remainder
`:.` The number exactly divides 2772 - 5 = 2767

Now, we have to find HCF of `1651, 2767`

Find HCF of 1651,2767

  
1
  
1651|
2767
 |
1651
 
1
 |
 
 |
1116
|
1651
|
1116
 
2
|
 
|
535
|
1116
|
1070
 
11
|
 
|
46
|
535
|
46 
|
|
75
|
46
 
1
|
 
|
29
|
46
|
29
 
1
|
 
|
17
|
29
|
17
 
1
|
 
|
12
|
17
|
12
 
2
|
 
|
5
|
12
|
10
 
2
|
 
|
2
|
5
|
4
 
2
|
 
|
1
|
2
|
2
|
|
0


`:.` HCF of given numbers (1651,2767) = 1



`:.` Required number = HCF of `1651, 2767 = 1`.






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