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Question

What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?


A

34

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B

37

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C

39

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D

33

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Solution

The correct option is D

33


The term 'greatest number that divides' indicates we need to find the HCF of the given numbers.
However to adjust the remainder 2, we will find the HCF after subtracting 2 from each of them.

H.C.F of (134 - 2) and (167 - 2).

H.C.F of 132 and 165
165 = 3 × 5 × 11
132 = 2 × 2 × 3 × 11

Taking all the common prime factors we get, highest common factor (165, 132) = 3 × 11 = 33

Hence, the required number is 33.


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