Write the cardinal number of the set of all integers $x$ which $\frac{60}{x}$ is a natural number.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept- We had to find the factors of 60 because the result of any fractional number is the natural number only if the denominator is the factor of the numerator.
As we know that x will subsist a representative of any number y exclusively if their y is impeccably separable ‘yx’. i.e. in distinguishable expressions we can say that ‘yx’ is a natural number.
So, for

60 x

to be a natural number,

x

must be a factor of 60.
Factors of 60 are illustrated as

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

and 60.
So, the total factor of 60 is 12.
Hence, x can have 12 different values.
As we witness that the cardinal number for a set is the complete number of possible rudiments of x.
Then set bearing values of x will have 12 rudiments.