What s d max value of n if 224! Divisible by 224^n?

• 224=2^5*7
  224! How many sevens....because we have less sevens than 32......I.e 2^5in 224 factorial we have 36 times 7
  So answer is 36...☑
• 8 years agoHelpfull: Yes(15) No(6)
• 224=(2^5)*7
  
  consider for 7
  224/7 =32
  32/7 = 4
  so n=32+4=36
• 8 years agoHelpfull: Yes(6) No(0)
• Prime factors of 224=2^5*7
  Now,no. of 7s in 224 is given by
  224/7 + 224/7^2 = 32+4 = 36
  And the no. 2s in 224 is given by
  224/2 + 224/2^2 + 224/2^3 + 224/2^4 +224/2^5 + 224/2^6 + 224/2^7 = 112 +56+28+14+7+3 = 220.
  Therefore no. of 2^5 in 224 = 44.
  Thus, n = 36.
  (minimum of two is taken)
  
• 8 years agoHelpfull: Yes(5) No(1)
• answer will be 36
  
• 8 years agoHelpfull: Yes(1) No(2)
• 36 is the correct answer
• 8 years agoHelpfull: Yes(0) No(1)
• (A1+A2+A3+A4+A5+A6+7)=30*7=210
  NOW AT TIME OF BIRTH OF YOUNGEST
  (A1-7)+(A2-7)+(A3-7)+(A4-7)+(A5-7)+(A6-7)+(7-7)=210-49=161
  NOW TOTAL 6 PERSON
  {(A1-7)+(A2-7)+(A3-7)+(A4-7)+(A5-7)+(A6-7)}/6= 161/6 ans...
• 8 years agoHelpfull: Yes(0) No(2)
• answer is : 36
  224 = 2^5*7
  224!/7 = 36 (so this is maximum power of 7 in 224!)
  but if one power of 7 so power of 2 is 5
  5*36=180 (power of 2 )
  224!/2= pow>180
  so clear ans is :36
• 7 years agoHelpfull: Yes(0) No(0)
• 224=(2^5)*7
  In 224! , 2 comes 109 times
  So (2^5) comes 20 times
  And in 224! , 7 comes 36 times
  Since 20 is less than 36 so the value of n is 20
  Ans is 20
• 7 years agoHelpfull: Yes(0) No(1)