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How many factors of 2^4 × 3^5 × 10^4 are perfect squares which are greater than 1?
How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?
CAT-2019 Question
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24 x 35 x 104
24 x 35 x 24 x 54
28 x 35 x 54
Now, for any number to be a perfect square, it must have an even number of factors.
So, if we consider 28, only powers of 0, 2, 4, 6, 8 can lead to perfect squares - 5 ways
If we consider 35, only powers of 0, 2, 4 can lead to perfect squares - 3 ways
If we consider 54, only powers of 0. 2, 4 can lead to perfect squares - 3 ways
So, total number of possibilities = 5 x 3 x 3 ways = 45 ways
Since we need to find the number of factors greater than 1,
Required number of ways = 45 -1 = 44 ways
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