numbser of divisors of 2⁵ . 3³ . 5⁵ . 6³ is
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Since the divisor is a perfect square, each prime factor must occur even number of times.
2 can be taken in 2 ways (2
0
or 2
2
)
3 can be taken in 3 ways (3
0
or 3
2
or 3
4
)
Similarly, 5 can be taken in 4 ways (5
0
or 5
2
or 5
4
or 5
6
) and 7 can be taken in 5 ways (7
0
or 7
2
or 7
4
or 7
6
or 7
8
)
Hence, total divisors which are perfect squares =2×3×4×5=120.
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