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Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case.

Solution:
Your problem -> Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case.

"Required number" = "HCF of " ( 147 - 77 ), ( 252 - 147 ), ( 252 - 77 )

= "HCF of " 70, 105, 175 = 35.

Factor of 70,105,175 are as follows...

 2 70 5 35 7 7 1

 3 105 5 35 7 7 1

 5 175 5 35 7 7 1

The HCF of a, b is the largest positive number that exactly divides both a and b.
Find HCF
 70 = 2 × 5 × 7 105 = 3 × 5 × 7 175 = 5 × 5 × 7 HCF = 5 × 7 = 35

HCF of 70,105,175 is 35

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