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AC and DC

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Find the product of all the divisors of 1440 and express it in the form of power of 2

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Q. Let the product of all the divisors of 1440 be P. If P is divisible by

24^{x}

, then the maximum value of x is

Q. Let the product of all the divisors of 1440 be P. If P is divisible by

24^{x}

, then the maximum value of x is

Q. The product of all divisors of N is

2^{40} 3^{10} 5^{10}

. Find the sum of digits of N.

Q. Find the number of proper divisors of the number

N = 2^{p} . 3^{q} . 5^{r}

. Also find the sum of
(i) all the divisors of N
(ii) all the proper divisors of N.
(iii) all the proper divisors of N which are multiple of 3.

Q. Product of all the even divisors of

N = 1000

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