Question

Let N = $2^2\times 3^3\times 7^4$

How many factors of $N^2$ which are less than N are not the factors of N?

• A. 91
• B. 92
• C. 98
• D. 94

Answer 1

The correct option is C 98

Given $N=2^2\times 3^3\times 7^4$

The number of factors of $N$ are $3\times 4\times 5=60$

$N^2=2^4\times 3^6\times 7^8$

The number of factors of $N^2$ are $5\times 7\times 9=315$

Among $315-1=314$ factors , half are less than $N$ , which implies $157$ factors of $N^2$ are less than $N$

Number of Factors of $N$ which are less than $N$ are $60-1=59$

Therefore number of factors of $N^2$ which are less than $N$ and not the factors of $N$ are $157-59=98$