Question 114

The greatest number that will divide 19,35 and 59 to leave the same remainder in each case is:

Solution

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Let the same remainder in every case be y

hence we need to find HCF of 19-y ,35-y and 59- y

using difference method ,

35 - y - 19 + y = 16

59 - y - 35 + y = 24

HCF of 16 and 24 is 8

hence 8 is the highest number which on dividing 19, 35 and 59 will leave same remainder

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