Question

If $\frac{a+2}{2}=\frac{b+4}{4}=\frac{c+6}{6}=12$, then number of factors of ${}^{\prime }ab{c}^{\prime }$

• A. $20$
• B. $40$
• C. $45$
• D. $50$

Answer 1

The correct option is B $40$

Explanation:-

Since acc. to given ques .

$\frac{a+2}{2}=\frac{b+4}{4}=\frac{c+6}{6}=12$

$\Rightarrow a=22,b=44,c=66$

$\Rightarrow abc=\left(22\right)\left(44\right)\left(66\right)=63888={11}^3\times 2^4\times 3$

Total no. of factors of composite numbers

$N=p^m{q}^n$ where N is composite number and $p$ and $q$ are prime numbers

Then, Total factors of $N$ $=(m+1)(n+1)$

Number of factors $=(3+1)(4+1)(1+1)=40$