Question

numbser of divisors of 2⁵ . 3³ . 5⁵ . 6³ is​

Answer 1

Answer:

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.