Bodhee Prep-CAT Online Preparation

CAT 2019 Quant Question with Solution 53

How many factors of $2^{4} \times 3^{5} \times 10^{4}$ are perfect squares which are greater than 1 ?

Show Answer

Correct Answer: 44

${{2}^{4}}\times {{3}^{5}}\times {{10}^{4}}={{2}^{8}}\times {{3}^{5}}\times {{5}^{4}}$

For perfect squares, we have to take only even powers of the prime factors of the number.

The number of ways 2’s can be used is 5 i.e. ${{2}^{0}},\ {{2}^{2}},\ {{2}^{4}},\ {{2}^{6}},\ {{2}^{8}}\ $

The number of ways 3’s can be used is 3 i.e. ${{3}^{0}},\ {{3}^{2}},\ {{3}^{4}}\ $

The number of ways 5’s can be used is 3 i.e. ${{5}^{0}},\ {{5}^{2}},\ {{5}^{4}}\ $

Therefore, the total number of factors which are perfect squares = $5\times 3\times 3=45$

But this also includes the number 1. Hence excluding 1, the required number is 45-1=44.

CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1

CAT 2019 Slot-2

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon