x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be  Choose the correct choice from the following answers
A) Between 1 and 10
B) Between 11 and 15
C) Between 15 and 20
D) Between 20 and 25
E) Greater than 25
Factorial 2 +1= 
<gadget id="calculator">2 +1</gadget>
<output>3</output>
3   smallest factor is 3==&gt;this is greater than 2   factorial 3 + 1=7   smallest factor is 7==&gt;this is greater than 3   factorial 4 + 1 = 25   smallest factor is 5==&gt;which is greater than 4   factorial 5 + 1= 121   smallest factor is 11==&gt;which is greater than 5   (note: i am excluding 1 as a smallest factor)   now by seeing this pattern you can figure out that..   (factorial x + 1)==&gt;smallest factor will always be greater than x   now coming to our problem   all even no.s between 2 to 50   2*4*6*8......*48*50   now take 2 from each number common.   2^25(1*2*3*4*5*......25)   or 2^25*factorial 25   now x+1= 2^25*factorial 25 + 1===&gt;clearly smallest factor will be greater than 25(as proved above)   ANSWGreater than 25R:Greater than 25
<result>E</result>
x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be