Self doubt on factorization

Question

In $900$ how many

$(A)$ Number of factors(divisors) are possible$?$

$(B)$ Number of Even factors are possible$?$

$(C)$ Number of Odd-factors are possible$?$

$(D)$ If the number is divisible by $25$ then a number of factors are possible$?$

$(E)$ Sum of factors$?$

$(F)$ Product of factors$?$

Comments

$N=p^{a}\times q^{b}\times r^{c}....$ where $p,q,r$ are prime number

Sum of factors $S_{n}=\frac{(p^{a+1}-1).(q^{b+1}-1).(r^{c+1}-1)}{(p-1).(q-1).(r-1)}$

please correct me if i'm wrong?

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$1)$ will be $(2+1)(2+1)(2+1)=27$

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Yes ma'am

I write all the answers in the above comment, you can see and verify it.

Answer 1

In 900 

900 = 2²×3²×5².

(A) Number of factors(divisors) are possible?

  (2+1) * (2+1) * (2+1) = 27

(B) Number of Even factors are possible?
  

 you need even divisor means  you must included  '2' and any no multiply with the 2 given even number 

(2)*(2+1)*(2+1) = 18

(C) Number of Odd-factors are possible?

 "didn't include '2' "

(2+1)*(2+1) = 9

(D) If the number is divisible by 25 then a number of factors are possible?

25 = 5 ²

Number must have the multiple of 5² then only it's divisible by 25 right ??

(2+1)*(2+1)*(1) = 9

(E) Sum of factors?

= (2 ⁰ + 2¹ + 2²)  x (3 ⁰ + 3¹ + 3 ²) x (5 ⁰ + 5 ¹ + 5 ²)

= $(\frac{2^{3}-1}{2-1}) X (\frac{3^{3}-1}{3-1}) X( \frac{5^{3}-1}{5-1})$

F) Product of factors = (Number) ^{no of factors /2}

                                                 = (900) ^27/2