A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.

Paresh Apr 6, 2020

#1**+2 **

\(\)4!=24

The factors of 24 are 1,2,3,4,6,8,12,24 and there are 8 of them

Therefore there is an \(\frac{8}{24}\) or \(\frac{1}{3}\) chance that the number chosen is a factor of 4!

Hope this helps!

-Ako

Ako180 Apr 6, 2020

#2**+1 **

In 4 factorial , it is 1*2*3*4 which factorizes to 2^3*3. This means is has 8 factors: 1,2,3,4,6,8,12, and 24. If a number is randomly chosen from 1-24, 8 out of the 24 would be factors of 4!. That means your answer will be 8/24=**1/3**.

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 6, 2020