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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$?$

1 Answer

Best answer
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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

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