Solution:
The number in question, 25×36×52, is a product of prime factors. We want to find how many of its factors are perfect squares. A number is a perfect square if all the exponents in its prime factorization are even.
Let's consider the general form of a factor of the number, which can be written as:
2a×3b×5c
Here, a,b, and c are integers that satisfy the conditions:
‌0≤a≤5
‌0≤b≤6
‌0≤c≤2
a can be 0,2 , or 4 - giving us 3 choices.
b can be 0,2,4, or 6 - giving us 4 choices.
c can be 0 or 2 - giving us 2 choices.
The total number of perfect square factors is the product of the choices for a,b, and c :
Total perfect square factors =3×4×2=24
Therefore, the answer is Option B: 24.
For this factor to be a perfect square, each of a,b, and c must be even. Thus:
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