Verified answer

Hi

THis product p is noted 30 ! ( factorial 30 )

I have no mathematic explanation ( no formula )

Between 1 and 30, you have 10 numbers which are multiple of 3 :

3, 6,9,..........., 24, 27, 30

3 = 3*1

6 = 3*2

9= 3*3

12 = 3*4

15 = 3*5

18 = 3*3*2

21 = 3*7

24 = 3*8

27 = 3*3*3

30 = 3*10

You find 14 times the digit 3, so, 3^14 is the greatest divisor of 30 !

Hope I helped

Bye !!!

Have your strategies artwork with ordinary arithmetic technique of removal tells me it is B I could come across a typical denominator ...SO the fast and ordinary way for me is purely multiply the three (from 2/3) with the denominator of each and every selection 3 x 11 = 33 = the common denominator. then i take the denominator from the two fractions and use it to make your strategies up the numerator for one and all sooo..11 x 2 = 22 and that i ought to have 22/33 for 2/3 then i exploit the different denominator to make your strategies up the relax fraction 11 x 3 = 33 (common denominator) and 3 x 8 = 24 and that i ought to have 24/33 properly (24/33) is larger than (22/33) so i finished at B and might use this technique to make your strategies up something , if any :)

C. 14

There are 10 multiples of 3 between 1 to 30,

So, 10

3 multiples of 9, viz. 9, 18, 27,

So, additional 3

and 27 is 3^3, so, another 1

10+3 +1 = 14

if you divide 1.2.3.4.5..... by 3^k , it'll only cancel off all the 3's in the numerator . so start grouping all multiples of 3 together (coz only these number will contain at least one 3) , u get 3,6,12,18,21,24,27 and 30 . now write all these numbers in terms of their prime factors .

3 = 1x3 ... 6=2x3 ... 9=3x3 ... 12=3x4 ... 15=3x5 .... 18=3x3x2 .... 21=3x7 ... 24=3x2x2 ... 27=3x3x3 ... 30=3x2x5 .... now count the number of 3's in all factors which equals 14 .. so 3^14 will be the factor of the given product ..