how can i find the greatest number that will divide 55, 127&175 so as to have the same remainder .

Asked by saraza | 27th Apr, 2010, 08:55: PM

Expert Answer:

Dear Student,

Let that number be K.and let the remainder left when dividing 55, 127 and 175 be x.

therefore we have,

55 = a1k + x      (1)

127 = a2k + x    (2)

175 = a3 + x      (3)

 

Subtracting (2) from (3), we get

48 = (a3-a2)k

=> k divides 48.

 

Subtracting (1) from (2), we get

72 = (a2-a1)k

=> k divides 72.

 

Subtracting (1) from (3), we get

120 = (a3-a1)k

=> k divides 120.

 

Now the greatest number k will obviously be the gcd of 48, 72 and 120.

By euclid's algorithm, we can easily find out the gcd of (48,72,120) = 24.

 

Hence, the greatest such number k = 24.

 

Also the remainder left when dividing 55 = 7.

the remainder left when dividing 127 = 7.

the remainder left when dividing 175 = 7.

 

 

Regards Topperlearning.

 

Answered by  | 27th Apr, 2010, 09:47: PM

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