If z is the product of all integers from 1 to 50, inclusive, what is the greatest integer x for which 5x is a factor of z?

• all the multiples of 5 should be written as a product of prime no's:
  5
  10=5*2
  15=5*3
  20=5*2*2
  25=5*5
  30=5*2*3
  35=5*7
  40=5*2*2*2
  45=5*3*3
  50=5*5*2
  so total no of 5's from 1-50 are 12 so the greatest integer can be 12
• 11 years agoHelpfull: Yes(18) No(1)
• To solve this, we must find the factors of 5 contained in z. They are: 5, 10 (5 * 2), 15 (5 * 3), 20 (5 * 4), 25(5 * 5), 30 (5 * 6), 35 (5 * 7), 40 (5 * 8), 45 (5 * 9), and 50 (5 * 5 * 2). Thus, we know there are 11 factors of 5 in p (don’t forget to count both 5’s in 25 and 50!). As a result, x must be 11.
• 11 years agoHelpfull: Yes(16) No(14)
• NO.OF 5'S IN 50!=12=>X SHOULD BE 5^11
• 11 years agoHelpfull: Yes(7) No(0)
• no of 5 in 50! are 12
  
  so x should be 5^11
• 11 years agoHelpfull: Yes(4) No(1)
• Answer should be x=5^11.......
• 11 years agoHelpfull: Yes(2) No(2)
• But there are 12 5s in 50!????
  Kindly xplain the soln
• 11 years agoHelpfull: Yes(0) No(4)
• the power of 5 is 12 and we get x as 12 when it is in the form of 5^x but here 5x hence the value of x is 10^11*2 since we should take power of 2 so that no of zeros are 10^12
• 11 years agoHelpfull: Yes(0) No(7)