total no of factors of 16!...????

• ans: 5376
  
  16! = 16*15*14*.......*3*2*1
  
  16! = 2^15 * 3^6 * 5^3 * 7^2 * 11^1 * 13^1
  
  total number of factors = (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1) = 5376
  
• 10 years agoHelpfull: Yes(29) No(4)
• 16! = 16*15*.......*4*3*2*1
  
  If we factorise every number we get :-
  
  16! = 2^16 * 3^6 * 5^3 * 7^2 * 13^1 * 11^1
  
  Hence, according to the formula, total number of factors of 16! is :-
  (16+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
  
  = 17*7*4*3*2*2
  
  = 5712 (Ans)
• 10 years agoHelpfull: Yes(9) No(8)
• 16! = 16*15*.......*4*3*2*1
  If we factorise every number we get :-
  16! = 2^15 * 3^6 * 5^3 * 7^2 * 13^1 * 11^1
  Hence, according to the formula, total number of factors of 16! is :-
  (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
  = 17*7*4*3*2*2
  = 5376 (Ans)
• 10 years agoHelpfull: Yes(3) No(0)
• 2^15*3^6*5^3*7^2*11^1*13^1= 16!
  
  now putting the formula:
  (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)=5376
• 10 years agoHelpfull: Yes(1) No(2)
• 2^4=16
  4+1=5
  1,2,4,8&16 can only divide 16
• 10 years agoHelpfull: Yes(0) No(7)
• 16=2^4
  4+1=5
  
• 10 years agoHelpfull: Yes(0) No(6)