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What number am I ?

I am a two-digit even number.

I am a common multiple of 6 and 7.

I have a total of 8 factors.

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answer is B.

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Detailed Solution

Concept- A factor is defined as a number that you multiply with another number to get a products.
Let

xy

be a two digit number
Given xy, there are multiples of x 6 and 7

x y = 6 \times 7 \times y \times z

= 42 \times y \times z

Also given it has 8 factors.
Let's check for 42 first

42 = 21 \times 2 = 2 \times 21

= 6 \times 7 = 7 \times 6

= 14 \times 3 = 3 \times 14

= 1 \times 42 = 42 \times 1

42 has 8 factors and a common multiple of 6 and 7 .
Hence, the correct option is 2.

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