Question

How many perfect squares are divisors of product 1!,2!,...9!

Answer 1

Answer:

18

Step-by-step explanation:

It is (1*1)(2*1)(3*2*1).....(9*8*7*...*2*1)

So , 1 occurs 10 times (twice in first term)

2 occurs 8 times. so , divisors(perfect sq.) from  2 are 4.(eg: 2*2 =perfect sq and so on).

3 occurs 7 times.

same;  div. obt.=3(quotient of no . of times /2)

4 occurs 6 times.

same;div obt.=3

5 occurs 5 times.

div. obt.=2

6 occurs 4 times.

d=2

7 occurs 3 times.

d=1

8 occurs 2 times.d

d=1 +1 (bcoz 8 has 4*2 and 4 is perfect)

9 occurs 1 time.

d=1 (9 is perf.)

Add=4+3+3+2+2+1+2+1

=18

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