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Problem based on remainders 1 (Updated On Tuesday, July 08, 2014)

What is the largest number which will divide each number 104, 221,377 to  leave the same remainder? 
1. 45      2. 39      3. 60    4. 70 5. 75 

Answer:
A number will divide 104,221,377 and this results in a common remainder.
Every number can be represented as - Number = divisor x quotient + remainder.
You are expected to find the largest divisor
Represent each number as per the equation given.

Let the divisor be (a) and the common remainder be (r)
The quotient will be different for each variable. Let the three quotients be k1 , k2 ,k3.
104 = k1. a + r  ---(1) 221 = k2. a + r ---(2) 377 = k3. a + r ---(3)
There are 3 equations but there are 5 variables. 
You have to use HCF to solve this problem.

Subtract (2)- (1) and (3)- (2)
117 = (k2-k1)a 156 = (k3-k2)a

What is 'a' wrt 117 and 156?
a is common factor of 117 and 156.

You can find 'a' by finding the HCF of 117 and 156. a =HCF(117,156) =39

39 is the largest number which can give the same remainder for 104,221,377


 

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