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