What is the probability that a randomly drawn positive factor of 60 is less than 7?

(A) 1/10
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
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For a Number \(N=a^p*b^q*c^r*...\)where a, b, c etc are distinct prime factors of n and p, q r are their respective exponents

The number of factors of \(N = (p+1)*(q+1)*(r+1)*...\) and so on

i.e. \(60 = 2^2*3^1*5^1\)

i.e. Number of factors of \(60 = (2+1)*(1+1)*(1+1) = 12\)

Factors of 60 which are less than 7 are \({1, 2, 3, 4, 5, 6}\)

i.e. Required Probability \(= 6/12 = 1/2\)

Answer: Option E

ALTERNATIVELY: One can find factors of a small number like 60 by simply writing all expressions in form of multiplication of two numbers
i.e. 60=
1*60
2*30
3*20
4*15
5*12
6*10

All the blue factors are less than 7 and total there are 12 factors hence required probability \(= 1/2\)
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